NTiA-REPORT-79-20

Ground Wave Propagation Over

Irregular, Inhomogeneous Terrain:

Comparisons of

Calculations and Measurements

R. H. Ott

L. E. Vogler

G. A. Hufford

u.s. DEPARTMENT OF COMMERCE

Juanita M. Kreps, Secretary

Henry Geller. Assistant Secretary

for Communications and Information

May 1979

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

ABSTRACT

v

xii

1

1.

2.

3.

4.

5.

6.

7.

8.

INTRODUCTION

MODIFICATIONS TO PROGRAM WAGNER

INTEGRAL EQUATIONS

COMPARISONS WITH MEASUREMENT

4.1 KBOL - Davidson Mesa Path

4.2 RADC Paths: KBLU to Junction and Water

4.3 ITS Measurements

SPACING/TIMING COMPARISON FOR

PROGRAMS WAGNER AND INTEQ

CONCLUDING REMARKS

ACKNOWLEDGEMENT

REFERENCES

1

2

3

6

15

18

44

69

SO

85

85

APPENDIX A: Effective Surface Impedance for a

Two-Layered Ground

APPENDIX Bl: USER'S GUIDE, LISTING AND SAMPLE OUTPUT 89

FOR PROGRAM WAGNER

APPENDIX B2: INPUT, LISTING AND SAMPLE OUPUT FOR IDe

PROGRAM INTEQ

iii

~igure

1.

LIST OF FIGURES

Page

Great circle path geometry for intregral equation. 4

2.

3.

4 •

5.

6.

7 •

8.

9.

10.

11.

Path profile (lower portion) and received signal in

dB above 1 ~V/m for 1 kW Effective Radiated Power)

for WGR-TV. Crosses denote measured spatial averages taken on 100 ft. mobile runs; circles denote

"residue-height gain" predictions (see text). WGR

antenna: 133 m above ground, 320 m above seal level.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW Effective Radiated

Power) for KCBS. Crosses denote measured median&.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kw effective radiated

power) for KBOL. Crosses denote measured 2.5 min.

averages on Dec. 9 and the circles those of Dec. 15.

Path profile (lOWe;~On) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for KBOL. Crosses and circles denote

measured 2.5 min. averages.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for KBLU. Crosses denote measured averages.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for KBLU. Crosses denote measured averages.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m .for 1 kW effective radiated

power) for KBLU. Crosses denote measured averages.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 2 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 1.618 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.520 MHz.

v

12

14

16

17

19

20

21

34

35

36
Figure

12. Path profile (lower portion) and received signal 37

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

fue~stired 2~5 fuin. aver~ges. Frequency = 0.412 MHz.

13~ Path profile (lowef portion) and :received signal 38

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

me~sured 2.5 min. averages. Frequency = 0.182 MHz.

14. Path profile (lower portion) and received signal 39

{in dB above 1 ~V/rn for 1 kW effective radiated

pdWSr) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.121 MHz.

15. Path profile (lower portion) and received signal 40

(in dB above i ~V/m fot 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

fueasured 2.5 min. averages. Frequency = 2 MHz.

16. Path profile (lower portion) and received signal 41

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canybhland§, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 2 MHz.

17. P~thprbfile (lower portion) andrebeivedsignal 42

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, path.

Cross~s denote measured 2.5 min. averages.

FreqUency = 2 MHz.

18. Path profile (lower portion) and received si~ 43

(ihdBabdv~ 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, p-ath.

Crbss~s denote measured 2.5 min. averages.

Frequency = 1.619 MHz~

19. Path profile (lower portion) and received signal 44

(in dB above 1 ~V/m for 1 kW effective radiated

pdwer) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 0.518 MHz.

20. Path profile (lo~er portion) and received signal 45

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 0.419 Maz.

vi
Figure

21.

22.

23.

24.

25.

26.

27.

28.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 0.161 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco,California,path.

Crosses denote measured 2.5 min. averages.

Frequency = 0.137 MHz.

Path profile tlower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 2 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective r~diated

power) for Santa Ritas, Arizona-, path. Crosses

denote measured 2.5 min. averages.

Frequency = 2 MHz.

Path profile (lower portion) and received signal

(in dB abovel ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 2 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 2 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 1.619 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 1.619 MHz.

vii

46

47

48

49

50

51

52
Figure

29.

30.

31.

32.

33.

34.

35.

36.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 0.518 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denoted measured 2.5 min. averages.

Frequency = 0.518 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 0.419 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 0.419 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 0.160 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for lkW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 0.160 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m fOr 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 0.137 MHz.

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages.

Frequency = 0.137 MHz.

Page

54

55

56

57

58

59

60

61

37. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Dry Lake, Nevada, path. Crosses denote

measured 2.5 min. averages. Frequency = 2 MHz.

Predictions made using PROGRAM INTEQ.

viii

62
Figure

38. Path profile (lower portion) and received signal 63

in dB above 1 ~V/m for 1 kW effective radiated

power) for Dry Lake, Nevada, path. Crosses denote

measured 2.5 min. averages. Frequency = 2 MHz.

39. Path profile (lower portion) and received signal 64

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Dry Lake, Nevada, path. Cross~s denote

measured 2.5 min. averages. Frequency = 1.619 MHz.

40. Path profile (lower portion) and received signal 65

(in dB above 1 ~~T/m for 1 kW effective radiated

power) for Dry Lake, Nevada, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.518 MHz.

41. Path profile (lower portion) and received signal 66

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Dry Lake, Nevada, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.419 MHz.

42. Path profile (lower portion) and received signal 67

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Dry Lake, Nevada, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.160 MHz.

43. Path profile (lower portion) and received signal 68

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Dry Lake, Nevada, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.137 MHz.

44. Path profile (lower portion) and received signal 70

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses

denote measured median. Predictions using PROGRAM

WAGNER, 100 m spacing intervals. At 20 km, the two

measured values correspond to two sites close to

the radial selected for comparisons

45. Path profile (lower portion) and received signal 71

(in dB above 1 ~V/rn for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM WAGNER.

46. Path profile (lower portion) and received signal 72

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM WAGNER.

ix
Figure Page

47. Path profile (lower portion) and received signal 73

(in dB above 1 ~v/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM INTEQ.

48. Path profile (lower portion) and received signal 74

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM INTEQ.

49. Path profile (lower portion) and received signal 75

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM INTEQ.

50. Nevada path at 2 MHz using PROGRAM WAGNER with 76

1 km spacing of observation points.

51. Nevada path at 2 MHz using PROGRAM WAGNER with 76

500 m spacing of observation points.

52. Nevada path at 2 MHz using PROGRAM WAGNER with 77

200 m spacing of observation points.

53. Nevada path at 2 MHz using PROGRAM WAGNER with 78

100 m spacing of observation points.

54. Nevada path at 2 MHz using PROGRAM INTEQ with 78

1 km spacing of observation points.

55. Nevada path at 2 MHz using PROGRAM INTEQ with 78

500 m spacing of observation points.

56. Nevada path at 2 MHz using PROGRAM INTEQ with 79

200 m spacing of observation points.

57. Nevada path at 2 MHz using PROGRAM INTEQ with 79

100 m spacing of observation points.

58. Nevada path at 137 MHz using PROGRAM WAGNER with 81

1 kmspacing of observation points.

59. Nevada path at 137 MHz using PROGRAM WAGNER with 81

500 m spacing of observation points.

60. Nevada path at 137 MHz using PROGRAM WAGNER with 82

200 m spacing of observation points.

61. Nevada path at 137 MHz using PROGRAM WAGNER with 82

100 m spacing of observation points.

x
Figure

62.

63.

64.

65.

Nevada path at 137 MHz using PROGRAM INTEQ with

1 krn spacing of observation points.

Nevada path at 137 MHz using PROGRAM INTEQ with

500 rn spacing of observation points.

Nevada path at 137 MHz using PROGRAM INTEQ with

200 m spacing of observation points.

Nevada path at 137 MHz using PROGRAM INTEQ with

100 m spacing of observation points.

xi

83

83

84

84
Table

I.

II.

III.

IV.

V.

LIST OF TABLES

Predictions/Comparisons For 9 Paths.

Measured received power in dBm, P (upper

number), and field strength in dBmabove

1 ~V/m, DBU (lower number), for the

designated frequencies and distances from

the transmitter along the Canyonlands path.

Measured received power in dBm, P (upper

number), and field strength in dBmabove

1 ~V/m, DBU (lower number), for the

designated frequencies and distances from

the transmitter along the San Francisco path.

Measured received power' in dBm, P (upper

number), and field strength in dBmabove

1 ~V/m, DBU (lower number), for the

designated frequencies and distances from

the transmitter along the Santa Rita path.

Measured received power in dBm, P (upper

number), and field strength in dBmabove

1 ~V/m, DBU· (lower number), for the

designated frequencies and distances from

the transmitter along the Nevada path.

xii

7

26

28

29

32
GROUND WAVE PROPAGATION OVER IRREGULAR, INHOMOGENEOUS

TERRAIN: COMPARISONS OF CALCULATIONS AND MEASUREMENTS

R. H. Ott, L. E. Vogler, and G. A. Hufford*

An algorithm (PROGRAM WAGNER) that evaluates HF

ground-wave attenuation over irregular, inhomogeneous

terrain is used to compare calculated field strengths

with observed measurements for 9 actual paths and

frequencies ranging from 120 kHz to 50 MHz. All

comparisons show encouraging agreement between calculations and measurement. The 20 MHz comparisons over

the Colorado Mountains provided a challenge for

PROGRAM WAGNER.

Key Words: HF-VHF groundwave prediction; integral

equation method; irregular terrain;

measurement comparisons; radio propagation.

1. INTRODUCTION

A method for calculating the ground-wave field over irregular, inhomogeneous terrain was developed by Ott (1970, 1971a),

and comparisons with alternative analytical methods were made

for idealized terrain profiles such as concave parabolas, sealand-sea paths, and single Gaussian ridges (Ott, 1971b, 1974).

The excellent agreement between methods like Fock currents for

concave surfaces, the classical residue series, and an integral

equation developed by Hufford (1952), and Ott's method based

upon an elementary function (closely related to the Sommerfeld

flat-earth attenuation function) for the parabolic wave equation provided encouragement for the usefulness of Ott's method

and the associated algorithm.

The computer program (called PROGRAM WAGNER) implementing

the method based upon the parabolic wave equation is described

in Ott (1971a). Improvements in the algorithm PROGRAM WAGNER

which have been developed are: 1) a linear -interpolation to

represent the terrain heights between input terrain heights

versus distance, and 2) the inclusion of an effective heightgain function to account for the influence of an elevated

*The authors are with the U. S. Department of Commerce, National

Telecommunications and Information Administration, Institute for

Telecommunication Sciences, Boulder, Colorado 80303.
transmitting and/or receiving antenna. The input terrain height

versus distance data can be obtained from existing digitized

profiles (Hopkins, 1977).

The purpose of the present paper is to describe certain

extensions and modifications of the original program, and also

to present a comparison of computed field strength values with

actual measurements obtain~d over nine particular paths and

frequencies ranging from 120 kHz to 50 MHz.

A draft new report on propagation over irregular, inhomogeneous terrain based on PROGRAM WAGNER was recommended in the

CCIR XIV Plenary Assembly in June 1978 in Kyoto, Japan as a

contribution to propagation by diffraction" and will be recommended to the Special Preparatory Meeting for GWARC-79 scheduled

for October 1978 in Geneva. In addition, several groups in this

country have implemented the computer algorithm at their facility.

For example, Hansen (1977) used PROGRAM WAGNER to estimate the

effects of a bluff along a path from Point Lorna in San Diego,

California to Point Mugu near Santa Cruz island. Recently

Monteath (1973) pointed out the use of our integral equation

program for solving the problem of propagation over irregular,

inhomogeneous terrain. Wait (1974) discusses the use of our

integral equation for cases where the geometry is not amenable

to mode matching.

2. MODIFICATIONS TO PROGRAM WAGNER

In order to compute fields over actual paths using the previous version of PROGRAM WAGNER, the terrain had to be fit with

some .form of analytic function. Past versions of WAGNER used a

series of Gaussian exponential terms to fit the actual terrain

data points. A detailed description of this method of terrain

fitting is given in an ITS Technical Memorandum of limited distribution, ERLTM-ITS 160 , by J. E. Herman and R. H. Ott.

Th;e new version of PROGRAM WAGNER uses a linear fit to the

input data points for the terrain elevation versus distance and

a 2-point approximation for the derivative or slope of the terrain versus distance.

-2....
Another modification of the original WAGNER is the inclusion

of an effective height gain function to account for the influence

of an elevated receiving antenna. The expression used is the

first two terms in the series expansion of the exact height gain

function arising from the smooth-earth diffraction residue

series, i.e., 1 + ik6h. Here, k denotes the wave number, 6 is

the normalized surface impedance, and h the receiving antenna

height. The approximation is valid for heights, h, to about the

first maximum in the height-gain pattern.

Finally, the modification to the integral equation for the

case of propagation over terrain having up to 2 layers in conductivity and dielectric constant versus depth was derived and

is given in Appendix A. This extension would allow the prediction

of ground wave field strengths for example in the caSe of permafrost or a forested and vegetated environment. However, the

mathematical results for layered ground have not been included

in the latest computer algorithm PROGRAM WAGNER.

3. INTEGRAL EQUATIONS

The derivation of the integral equation used in the algorithm PROGRAM WAGNER is given in Ott (1970, 1971). The final

result is

f (x ) = W(x , 0) - If 1f (g) e-ikw (x , 0 {y' (0 W(x , g) - y (~:~y ( g)

o

(1 )

where x, g, y(x) and y(g) are defined in Figure 1 and f(x) is the

field normalized to twice the free-space field. The factor

(6-6r) arises in mixed-path problems. The factor 6r is constant

with distance and is the relative value of the normalized surface

impedance. This factor is computed using the values for 0 and

E for the first section of a mixed path. The factor 6 varies

r

with distance in a mixed path problem. The variation of 6 with

x may be continuous or contain abrupt changes. The factor

(6-6 ) is zero for a single section path. The remaining factors

r

in (1) are defined as

-3-
Figure 1.

y

TRANSMITTER

ORIGIN ,~----~x-------

Great circle path geometry for integral equations.

y2(X)

2x

W(X,~) = 1 - i (TIP w(-Iu

u = P {l - Y(X)_y(~)}2 ;~ < X ~(X-~)

w (-/u) = e - u e r f c (ilil )

1 00

= in f

-00

2

e-t dt (Abramowitz and Stegun, 1964);

/"u+t

vertical polarization

horizontal polarization;

-4-
i 18(10 3 ) 0

n = €r - f(MHZ-)---;

f = frequency, in MHz;

o = ground conductivity;

€r = dielectric constant.

Equation (1) gives the integral equation for the attenuation function normalized to twice the free-space field

The derivation of the integral equation used in the algorithm PROGRAM INTEQ (given in Appendix B2) is described by

Hufford (1952), and the final result is

f(x)=l -Ajf(O [ll+y'(Oo (2 )

y(x)-y(F;,) ] exp{ik/2(p _P _P )} [x ]1/2 de

x-F;, 1 2 0 F;,(x -F;, ) s

(3 )

(4)

2(r -x)-</>(x), o

- </> (x)+</> (0

- </>(x)

2 [y(x)-ha]

x

2 [y (F;,) -hal

F;, - </>(F;,) 2(rl-F;,)-</>(F;,),

[y (x) -y (0] 2

x-F;, P = 2

where

</>(x) = - 2 y'h +

o a

x

1 [y' (0]2 dF;"

o

( 6a)

y~ = y' (0 I

F;,=o,

(6b)

and the distances Po' PI' and P2 correspond to the first two terms

in the binomial expansion for the distances r o' r l, and r 2 shown

in Figure 1 minus the distance the wave travels along the surface

of the terrain.

-5-
The numerical analysis used to solve (1) and (2) is significantly different, and the form for the integral equation in (1)

has the potential of being numerically more efficient because the

integral part of the integral equation is subtracted from a function, W(x,O), that decays with distance according to the Sommerfeld flat earth attenuation function. For example, if a = .01

Slm, E = 10, frequency = 10 MHz, and x = 1 km, then

r

0.024 + iO.042, P 4.44 - i2.47, and W(x,O)~ -0.077 + iO.064.

Suppose the exact value for the magnitude normalized attenuation,

If(x) I, is 0.11. Then using the form for the integral equation

in (1) requires only one significant figure from the integral

portion whereas the form in (2) requires two significant figures.

However, in the actual examples considered in this study it was

not clear that the algorithm PROGRAM WAGNER was more efficient

than the algorithm PROGRAM INTEQ. In principle, PROGRAM WAGNER

should allow a larger spacing for the observation points, x, to

achieve a convergent solution than PROGRAM INTEQ. The present

versions of both algorithms indicate that PROGRM4 INTEQ is at

least a factor of 4 faster in computation time than PROGRAM

WAGNER. Obviously, the techniques used to code the integral

equation in (2) need to be considered in coding of (1) but this

is well beyond the scope of this report.

4. COMPARISONS WITH MEASUREMENT

Table 1 summarizes the comparisons of the integral equation

predictions and the measurements, together with the source of the

latter. The spacing of points refers to the variable x in (1)

or (2) and is the distance projected on a horizontal plane. The

computational time is for a CDC 6600 computer. The spacings

used were not necessarily optimum and were arrived at by decid~

ing the 100 meter spacing yielded reasonable agreement for the

WGR-TV path from Buffalo, New York. When the terrain was relatively flat, spacings as large as I km were used.

-6-
TABLE I

Predictions/Comparisons for 9 Paths

740 kHz CBS Radio (1971)

Frequency" Reference

Canyonlands, UT 2.0 MHz

adjacent to Canyonlands National Park

Transmitter (KBOL) in 1490 kHz

Boulder, south over

Davidson Mesa

Timc(sec.) Figure No.

1213 2

(596 pts. )

113 3

(144 p t s , )

116 4

(194 pts. )

82 5

(194 pts. )

203 6

(294 p t s , )

55 7

(154 p t s , )

56 8

(154 p t s , )

620 9

(486 pts. )

609 10

(486 p t s , )

611 11

(486 p t s , )

636 12

(486 p t s , )

x-spacing

O.1{O.1)48.5km;48.58km

o. 5 (0 • 5 ) 7 2 km

O.5(0.5)41km;41(0.1)45km

O.1(0.1)4B.5km;48.58km

1(1)100m;100(50)1000m

1(1) 47km;47(0.25)155km

0.1(0.1)19.3km;19.31km

(0=0.008 s/m)

0.1(0.1)19.3km;19.31km

(0=0.015 s/m)

0.l(O.1)48.5km;48.58km

45(0.5)61km;6l(O.1)73km

73(0.5)83km

O.5(O.5)46km;46(O.1)48.5km;

48.6(0.5)67km

O.5(O.5)46km;46(O.l)48.5km;

48.5(O.5)67km

0.l(O.l)48.5km;48.S8krn

Heckscher, J. (1977)

Same

W. A. Kissick, et al.,

(1978)

Same

Same

W. A. Kissick, et al.,

(1978)

59.75 MHz Head, H.T. (1958)

(horizontal

polarization)

518

1.619 HHz

.419

Path

Transmitter (WGR-TV)

in Buffalo, NY-over

Lake Erie toward

Cleveland, Ohio

Transmitter (KCBS)

north of San Francisco

Bay, south through San

Francisco, over Santa

Cruz Hountains

Transmitter (KBLU) in 560 kHz

Yuma, AZ, beyond

Tinajas Altas

Mountains toward Mexico

Canyonlands, UT

adjacent to Canyonlands National Park

Canyonlands, UT

adjacent to Canyonlands National Park

Canyonlands, UT

adjacent to Canyonlands National Park

I

.....,J

I
Table I (Continued)

Path Reference x-spacing Time(sec.) Figure No.

Canyonlands, UT

adiacent to Canvonla~ds Nation~l ~ark

Canyonlands, UT

adjacent to Canyonl~nds National Park

Canyonlands, UT

adjacent to Canyonlands National Park

Canyonlands, UT

adjacent to Canyonlands National Park

Frequency

.180

.120

2.0

2.0

w. A. Kissick, et al.,

(1978)

Same

Same

Same

0.1(0.l)48.5kmi48.58km

0.1(0.1)48.5krn;48.58krn

0.1(0 1)48.5km;48.58km

(Colorado River a & c)

0.1(0.1)48.5krn;48.58krn

(ECAC profile data)

632

(486 p t s , )

625

(486 p t.s , )

608

(486 p t s , )

679

(486 p t s , )

13

14

15

16

0.1,0.2krniO.23(0.5}11.23krn

0.1,0.2kmiO.23(0.5)11.23km

I

CO

I

From Mare Island,

Valejo, CA south

over San Francisco

Bay over Marin

Peninsula

From Mare Island,

Valejo, CA south

over San Francisco

Bay over Harin

Peninsula

2.0 MHz

1.619 MHz

Same

Same

57

(158 p t s . )

11.41(O.l)12.01km;12.07(0.5)18.57krn

18.72(0.1)20.22km;20.31(0.5)26.81km;

26.94(0.1)28.44km;28.52(0.5)31.02km;

31.48(0.1)37.28km;37.3krn

57

(158 p t s , )

11.41(0.1)12.01km;12.07(0.5)18.57km;

18.72(0.1)20.22km;20.31(O.5)26.81km;

26.94(0.1)28.44km 28.52(0.5)31.02km;

31.48(0.1)37.28km;37.3km

17

18

Same

Same

Same

Same

0.518 MHz

0.419 MHz

0.161 MHz

0.137 MHz

Same

Same

Same

Same

Same

Same

Same

Same

59

(158 p t s . )

59

(158 pts.)

58

(158 pts.)

56

(158 p t s , )

19

20

21

22
TABLE I (Continued)

Path Frequency Reference x-spacing Time (sec.) Figure No.

Santa Ritas, AZ 2.0 MHz w. A. Kissick, et ale , O.l(O.l)lkm; 1(0.5)7km 72 23 near Greenval1ey, AZ (1978) 7(0.1)20km; 20(0.5)30km (172 p t s , )

and adjacent to AZ (0 change at 16.40 km)

Experimental Range

Same Same Same o•1 (0 . 1) 30 krn 210 24

(0 change at 12.95 km) (300 pts.)

Same Same Same Same 106 25

(measured values for 0) (166 pts. )

Same Same Same Same 7 26

(Two sectio~ flat earth) ( 49 ,pts.)

Same 1.619 MHz Same O.l(O.l)km; 1 (0.5) 7 km 70 27

7(0.1)20km; 20 (0.5) 30 km (172 pts. )

(conductivity from geological maps)

(0 change at 16.40 km)

I Same Same Same 0.1 (0.1) 1 kIn; 1(0.5) 7 km 97 28

\0 7(0.1) 20 kmi 20(0.5) 30 km (172 pts. )

I conductivity from geological maps)

(except 0 change at 12.95 km)

Same 0.518 MHz Same Same 71 29

'(except 0 change at 16.40 km) (172 pts. )

Same Same Same Same 97 30

(except o change at 12.95 km) (172 pts. )

Same 0.419 MHz Same Same 70 31

(except o change at 16.40 km) (172 p t s , )

Same Same Same Same 107 32

(except (J change at 12.95 km) (172 p t s , )

Same 0.160 MHz Same Same 69 33

(except 0 change at 16.40 km) (172 pts.)

Same Same Same Same 106 34

(except 0 c,hange at 12.95 km) (172 p t s , )

Same 0.137 MHz Same Same 69 35

(except 0 change at 16.40 km) (172 pts. )

Same Same Same Same 108 36

(except 0 c!1ange at 12.95 km) (172 p t s . )
TABLE I (Continued

Time (sec.) P-'['gllreNO:-

263 38

(261 p t s. )

263 39

(261 p t s, )

254 40

(261 pts , )

259 41

(261 pts.)

267 42

(261 p t s, )

262 43

(261 p es . )

599 44

(505 p t s , )

677 45

(600 p t s , )

913 46

(600 p ts . )

59 47

(304 p t s , )

186 48

(595 pts. )

445 49

(996 pts.)

I

.......

o

I

Path

Dry Lake, NE ,

Transmitter on east

slope of Highland

Peak to Dry Lake

Valley

Same

Same

Same

Same

Same

Same

Colorado Mountain

Data toward Berthoud

Pass Campground

Same

Same

Same

Same

Same

Frequency

2.0 MHz

Same

1.619 MHz

0.518 MHz

0.419 MHz

0.160 MHz

0.137 MHz

20.084 MHz

Same

Same

Same

Same

Same

Reference

W. A. Kissick, et ale

(1978)

Same

Same

Same

Same

Same

Same

M. E. Johnson, et a~.

(1967)

Same

Same

Same

Same

Same

x-spacing

0.1(0.1) 15km;15{O.5)21 km;

21(0.1)23km;23(O.5)42km

42(0.1)44.5km:44.5(0.5)52km;

52.46 km

(PROGRAl-1 IN'rEQ)

Same

(PROGRAM WAGNER)

Same

Same

Same

Same

Same

0.1(O.l)50.4kmi50.46km

0.05(0.05)30km

o•01 ( 0 • 01) 6 km

O.46(0.1)30.76km;

(PROGRAM INTEQ)

0.26 (0.05) 29.96 km

(PROGRAM INTEQ)

o•05 (0 " 01 ) 10 km

(PROGRAM INTEQ)

8

(147 pts . )

37
The algorithm, PROGRAM WAGNER, is best suited to propagation frequencies below VHF. Also, because of problems in maintaining numerical accuracy during the integration process, predicting attenuation for vertical polarization is usually more

successful than for horizontal polarization.

In the upcoming comparisons, the ordinate scales are in the

familiar dB~/kW, which is to say the field intensity measured in

dB above l~V/m and normalized to the case of 1 kW radiated from

a (vertical) half-wave dipole.

To test what might be considered an extreme case for the

applicability of WAGNER, a path near Buffalo, New York, was

chosen (Head, 1958). Field strength measurements were available

along a radial from WGR-TV over a path that extended out to about

155 km. The station transmitted horizontally polarized waves at

a frequency of 59.75 MHz. The initial portion of the path (about

47 km) was over Lake Erie, with the remaining portion over land

containing variable terrain features. A plot of the path profile

is shown in the lower part of Figure 2; it should be noted that

the irregularity of the terrain is greatly exaggerated because

of the expanded height scale.

The predicted effective radiated power in Figure 2 was obtained using a version of PROGRAM WAGNER which used a series of

Gaussian terms to fit the terrain profile, using PROGRAM

TERMAP. Fifty-eight terms were used in the terrain fit, with

the difference between fit and actual terrain data points being

everywhere less than about 27 m. The predicted field, represented by the solid line, is shown in the upper part of Figure 2.

The abrupt change at about 47 km is caused by the passage of

the wave from the smooth surface of Lake Erie (with assumed

dielectric c6nstant = 81 and conductivity = 0.01 Slm) to the

land (with dielectric constant = 15 and conductivity = 0.03 S/m).

Measured values are represented by XiS that start near the

shore of the lake and are plotted at various distances over the

land portion of the path. The upper end of the vertical line

-11-
I

,tt,

00

00

o

i

i

!

I

---+----+------'~---j

I

!

70~-

20 1-----+------+---I----+--.\lI--\,I----'~~-+±___l

90

-

1*

10 f---+---+---+--f----f---+--f-=f-I-*-l

20 00

WGR-TV

216 deg Radial

Distance in Kilometers 140 154.5

Figure 2. Path profile (lower portion) and received signal in

dB above 1 ~V/m for 1 kW Effective Radiated Power)

for WGR-TV. Crosses denote measured spatial averages

taken on 100 ft. mobile runs; circles denote

"residue-height gain" predictions (see text). WGR

antenna: 133 m above ground, 320 m above sea level.

-12-
through each X is the maximum field that was measured during a

100-ft. mobile run at each receiving site; the lower end is the

minimum observed field and the XiS are plotted at the median

values.

The calculated field appears to follow the general trend of

the observed values although individual points are not predicted.

One reason for this, of course, could be that local terrain

effects at the measurement sites (e.g., buildings, telephone

wires, etc.) greatly influence the received field. There is

also some indication, especially in the first few measurements

near Lake Erie, that complex interference effects not accounted

for by the simple ground-wave model are operating.

Figure 2 also 'shows a set of- points, denoted by circles,

that give a predicted field obtained by multiplying the classical residue series over a smooth sphere (with E = 15 and a =

0.03 S/m) by a "terrain-height gain" function, 1 + ikL1y, where

y is the terrain height above the sphere. This was included,

not as a recommended prediction model, but merely as a matter of

interest to show an attempt at a simple approach to the problem

of irregular terrain propagation. It is apparent that the

received fields depend significantly on the intervening terrain

and not just the terrain height at the receiving point.

A second comparison of calculations and observations was

made on a path in the San Francisco region (CBS Radio, 1971).

Measurements were available on a radial from KCBS, a station

transmitting vertically polarized waves at a frequency of 740 kHz.

Figure 3 shows the path profile, measured field strength values,

and prediction curve over a path of about 73 km. The terrain

function deviated from the actual terrain data by about 40 m at

the most using PROGRAM TERMAP. As can be seen, the prediction is

well in aooord wi th the observed data except for the end of the

path. Whether the disagreement in this region is because of

inaccurate values of electrical ground constants or, perhaps, the

wrong assumption for the effect of atmospheric refraction is

not known. The following table shows the ground constants used

over various portions of the path.

-13-
90

80

70

\

x

\

x

\

~\X lISt, x

I\.

X

'~ ~x x V'

x tx~x ~·x

x Xx

x ~- '" x

x x

x x XVV~

x x x

60

110

100

120

400

300

(J)

0+- 200

(l)

100

00 Distance In Kilometers

KeSS

170 deg Radial

12.7

Figure 3. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW Effective Radiated

Power) for KCBS. Crosses denote measured medians.

-14-
Distance (km) E: a (8/m) -

to 19.19 15 0.01

21.98 81 5

22.50 15 0.03

25.05 81 5

30.41 15 0.03

37.72 81 5

72.73 15 0.008

In both of the examples presented here, a standard "4/3-earth"

atmosphere was assumed. The computer program is capable of including other values of constant atmospheric rfi-Y bending through

the use of the effective earth's radius cbncept.

It should again be noted that the first few measurements

near the transmitting end of the path indicate a more complex

interference mechanism than is assumed in the present model.

4.1 KBOL - Davidson Mesa Path

Two sets of field strength measurements were taken along a

radial running from station KBOL in Boulder, Colorado (f = 1490

kHz, vertical polarization), southeast towards the Davidson Mesa

area. The terrain profile is shown in the lower portions of

Figures 4 and 5. The measurements P , in terms of received power m

in dBm, were taken on Dec. 9 and Dec. 15, 1977.

d(km) P (12/9) P (12/15) d(km) P (12/9) P (12/15) m m m m

1.75 -43 8 -47.4 9.92 -62.5 -64.0

3.63" -58.3 -59.1 10.81 -65.5 -66.0

5.42 -56.5 -57.4 14.57 -68.0 -68.7

6.53 -56.4 -58.1 15.02 -68.2 -69.7

8.61 -61.4 -62.6 19.31 -70.2 -74.1

Because the absolute level of the radiated power from the

transmitter, Pt , was not known, the data were adjusted so that

the first measured point (at d = 1.75 km) agreed with the WAGNER

calculated value at this distance.

-15-
Freq. (MHz) = 1.490

O~~ SIG~~ EPS

19.32 .008000 15.0

1301+-----+----+-------..-----1

:e::- .. '":====*=======P====~====::=:

:85:

:8::

I

5

Boulrler, Davidson Mesa

C

X{km)

I

:5

Figure 4. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for KBOL. Crosses denote measured 2.5 min.

averages on Dec. 9 and the circles those of Dec. 15.

-16-
:lO Freq. (MHz) 1.490

D~'1 SW14 EPS

19.52 .015000 15.0

150ll----t-----+-----...-----

120 It----t-----+-----+-----~

100r----.::.'+------+---------1-

80r----lr-----+-----+.:::::::::::::~

90r-----+--4-ll:-:------l----J

IIOiT---r------+-----+----J

<,

r:Q

'D

:85:

:8::

I

5

Boulder, Davidson, Mesa

C

X (krn)

I

:5

Figure 5. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for KBOL. Crosses and circles denote

measured 2.5 min. averages.

-17-
0 = 0.008, E: = 15 0 = 0.015, E: = 15

d(km) DBU (12/9) DBU (12/15) DBU (12/9) DBU (12/15)

1.75 105.9 105.9 107.0 107.0

3.63 91.4 94.2 92.0 95.3

5.42 93.2 95.9 94.3 97.0

6.53 93.3 95.2 94.4 96.3

8.61 88.3 90.7 89.4 91.8

9.92 87.2 89.3 88.3 90.4

10.81 84.2 87.3 95.3 88.4

14.57 81.7 84.6 82.8 85.7

15.02 81.5 83.6 82.6 84.7

19.31 79.5 79.2 80.6 80.3

Figures 4 and 5 show the plots of predictions and measurements, the X's representing the measurements of Dec. 9 and the

circles those of Dec. 15. The measurements compare favorably

with calculations when a conductivity of 0 = 0.015 S/m is

assumed (Fig. 5). This is understandable since the Boulder path

is more over a "plains type" region (corresponding to 0 = 0.015)

rather than the adjacent foothills (0 = 0.008).

The measurements at the 3.6 km site are some 5 to 8 dB away

from prediction, but this is believed due to the fact that this

site (and only this site) was located in the midst of high

buildings and considerable traffic congestion.

4.2 RADC Paths: KBLU to Junction and Water

Rome Air .Development Center (Heckscher, 1979) has made a

number of field strength measurements in an area southeast of

Yuma, Arizona using as a source the Yuma commercial broadcast

station KBLU (560 kHz). The measurement sites are along jeep

roads that run in various directions throughout the area.

Although no series of measurements are strictly along a radial

from KBLU, some are approximately so. Two series were found in

the southern-most sector, and path profiles were determined from

USGS maps along two radials from KBLU. The profiles are shown in

the lower portions of Figures 6, 7, and 8. Path #1 (Fig. 6)

crosses a minor ridge (Vopoki Ridge) at about 45 km and, later

on, a higher ridge (Tinajas Altas Mtns.) at about 65 km. Path #2

(Figs. 7 and 8) crosses Vopoki Ridge also at about 45 km but

nearer the southern end.

-18-
Freq. (11Hz) 0.560

01('1 51""4 EP5

41." .020000 10.0

44.87 .000010 8.0

GI. II .020000 10.0

72.55 .000010 8.0

85.00 .020000 10.0

120,----.-----,-----.--,------ ,

\

'0 <,

a:l

'D 80 -_._- r~

I

I

'. -_._- .-t..

i

I

G: -. -- i----tI

I

50

:'::

12;;

I.".

§

'" a: s: .. 'n'"Q)

.c o~;

1,"

2"

2:

FBLt:

Figure 6. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for KBLU. Crosses denote measured

averages.

-19-
Freq. (MEz) = 0.560 120 --

x

i x x x x i

~- -----~-------+-----

---l~-,=:======:=:==-...L-----l.-.J

I

70 II

I

GO 1 _

80 -- -------+---f----+-::::::::........d.,,--4t--I---

OKM SIGM. EPS

4&.04 .020000 10.0

48.11 .000010 8.0

G7.00 .020000 10.0

5"..

... -"

,,,1

I .~'" I .c 2:: .....

x(km)

oil

KBLU

Figure 7. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for KBLU. Crosses denote measured

averages.

-20-
Freq. (11HZ) = 0.560

DI<ll 51'"4 EP5

67.00 .020000 10.0

110 rt---t----t----t---t---.:-,...-----.---I

100 r-T--t----t---t---t-,..--+---+--I

<,

l:Q

't:l

9°t---r"-+---+---+----+---_~

80 r--t-----t---t--=:::""'-o:::b---tt-+---+---l

5..

"

.,.

-..

KBLI;

Figure 8. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for KBLU. Crosses denote measured

averages.

-21-
The measurements corresponding to these two radials are

tabulated below in terms of the field intensity, E(mV/m),

measured at each location times the distance, d(km), from the

transmitter.

Path #1 Path #2

d(km) E·d(V) d(km) E· d (V) d(km) E-d(V)

75 38 41 205 50 178

77 52 43 196 52 185

78 55 44 204 54 192

80 62 46 223 57 193

81 68 48 267 61 204

83 72 49 243 64 180

From other measurements nearer the transmitter, E-d was

found to approach a value of about 250. Thus, in order to

compare with the WAGNER predictions in DBU, the measurements

obey the relationship

DBU = Eo + 20 log am = 112.94 -20 'log d(km) + 20 log am' (3)

where E is the reference field used in WAGNER and a = (E·d)/250 0 m

is the attenuation at each receiving site. The values of measured DBU for each path are given in the following table:

Path #1 Path #2 -- --

d(km) DBU d(krn) DBU d (krn) DBU

75 61.6 43 78.2 52 76.0

78 61.9 44 78.3 54 76.0

80 62.8 46 78.7 57, 75.6

81 63.5 48 79.9 61 75.5

83 63.7 49 78.9 64 74.0

PROGRAM WAGNER was run for Path #1 using the following

electrical ground constants:

d(km)

0-41.4

41.4-44.9

44.9~61.1

61.1-72.5

72.5-83.0

c

10

8

10

8

10

-22-

a (S/rn)

0.02

10- 5

0.02

10- 5

0.02.
The conductivity value of a = 0.02 represents the nearly level,

sandy portions of the area and was obtained from RADC on-site

-5 measurements. The values of a = 10 and E = 8 represent the r

conductivity and dielectric constant of the rock composing the

mountains and ridges of the area. The type of rock was determined from a geological map of Arizona, and a and E were

r

obtained from tables in a paper discussing ground constants of

various rock materials (Ring, 1958).

Figure 6 is a plot of predicted DBU from WAGNER (the solid

curve) for Path #1, together with measured DBU represented by

crosses. The last six measurements, which were taken along this

profile, appear to agree very well with prediction. The first

six crosses are measurements taken along Path #2 but plotted

here because of the near proximity and similarity of terrain for

the two paths in this area. These measurements do not agree as

well because of slight differences between the two profiles.

Path #2 was run on WAGNER with the following values for

electrical ground constants:

d(km)

0-46.0

46.0-48.1

48.1-67.0

E

r

10

8

10

a(S/m)

0.02

10- 5

0.02 .

Figure 7 shows the WAGNER prediction together with the measurements taken along this radial. The abrupt drop in predicted

field at.about 46 km is due to the change in ground constants at

this point. Because this radial crosses Vopoki Ridge at its

southern-most end where the ridge merges into the surrounding

plain, it was decided to run WAGNER again for this same profile

using the values E = 10 and a = 0.02, throughout the length of

the path. The result ~s shown in Figure 8. The better agreement

between prediction and measurements would indicate that the

received signal was travelling mostly over terrain characterized

by a conductivity of a = 0.02.

-23-
4.3 ITS Measurements

In the first half of-1978, signal strength measurements

were made by ITS (Kissick et al., 1978) along four different paths

located in the western part of the U.S. An attempt was made to

locate the paths in areas where access roads provided numerous

sites along the radial at which measurements could be taken.

The four paths and their location designations are~

(1) Canyonlands: Canyonlands National Park in

southern Utah;

(2) San Francisco: a path in the bay area of

San Francisco, California;

(3) Santa Rita: located near the Santa Rita

Mountains of southern Arizona;

(4) Nevada: a path west of Pioche, Nevada.

Measurements of received power at six different nominal

frequencies (2000, 1600, 500, 400, 200, 100 kHz) were recorded

at each site along the four paths. In figures 4 through 43 the

measured values denote the average of about 256 samples taken over

a period of about 2.5 minutes. In order to compare the measurements with the output of WAGNER in terms of field-strength in

decibels above 1 ~V/m (designated DBU), the following relationship is used:

DBU = 139.37 + 20 log f MHz - Pt + Pm (4)

where P is the measured received power in dB above 1 mW and

m

P

t

is an unknown constant (for each frequency run). To adjust

the DBU such that the first measured point (or some chosen

one) equals the WAGNER DBU prediction at that distance, d,

solve (20) for Pt :

Pt = 139.37 + 20 log f MHz + Pm(d=dl)-DBU(WAGNER at d=dl)=const.

(5)

The remaining DBU are then calculated from (4).

-24-
In general, values of electromagnetic ground constants

were determined from geological maps of the areas involved in

conjunction with tables of conductivity and dielectric constant

contained in a paper by Lytle (1974). Estimates of a and E for

various types of rocks ~re given in the tables, which values were

then used for the appropriate segments of the radio path as

determined by the geological maps. The one exception to this

procedure was in the case of San Francisco where much of the

path was over water. For this path, sea water values were used

over water and FCC suggested values were used for the portion

over land. We felt the FCC maps were more appropriate for

portions of this path which went over swampy regions where the

soil type was difficult to identify.

Canyonlands

Measurements were taken at 31 sites along a 45 km radial.

At some of the sites, signal records for particular frequencies

are missing; however, in general it was possible to obtain

measurements for all 6 frequencies at each site. A tabulation

of the site distances (from the transmitter), the received

power levels (at the 6 frequencies), and the values of DBU

used to compare with WAGNER calculations are shown in Table II.

The constant values, Pt, for each frequency were determined from

the first site at d = 1.16 km.

Figures 9 through 14 show comparisons of measurements

(denoted by crosses) with WAGNER predictions for the 6 frequencies. The lower portion of each figure shows the terrain

profile of the Canyonlands path with the terrain height above

mean sea level in meters versus the distance in kilometers.

Since the geological formations appear to consist almost

entirely of various types of sandstone, a constant

a = 0.004 Sim and E = 5 was assumed throughout the path.

-25-
Table II. Measured received power in·dBm, P (upper number) , and field strength in dB above 1 llV/m, flBU (lower number) , for the designated frequencies and distances from the

transmitter along the Canyonlands path.

f (MHz) 2.00 1.618 0.520 0.412 0.182 0.121

d(km)

1.16 -28.6 -25.9 -41.2 ·44.9 -53.9 -60.3

108.8 109.9 111.7 111.8 111.8 111.8

1.44 -31.4 -28.8 -43.9 -48.3 -57.4 -64.1

106.0 107.0 109.0 108.4 108.3 108.0

2.00 -38.1 -33.0 -50.0 -54.2 -62.5

99.3 102.8 102.9 102.5 103.2

3.19 -39.1 -49.4 -55.1 -65.2 -72.7

96.7 103.5 101.6 100.5 99.4

4.69 -50.2 -44.8 -52.7 -57.2 -62.2 -72.5

87.2 91.0 100.2 99.5 103.5 99.6

6.75 -52.5 -48.3 -58.1 -60.5 -70.8 -78.3

84.9 87.5 94.8 96.2 94.9 93.8

7.22 -50.8 -56.3 .... 60.0 -65.8 -72.7

86.6 96.6 96.7 99.9 99.4

9.75 -56.5 -51.9 -60.8 -62.8 -70.7 75.4

80.9 83.9 92.1 93.9 95.0 96.7

13.75 -64.5 -67.9 -71.0 -78.9 -80.8

71.3 85.0 85.7 86.8 91.3

1"4 • 06 -73.2 -65.4 -71.8 -71.8 -79.3 -81.3

64.2 70.4 81.1 84.9 86.4 90.8

14.72 -71.0 -65.7 -68.5 -69.1 -74.5 -79.5

66.4 70.1 84.4 87.6 91.2 92.6

19.62 -69.4 -67.0 -69.8 72.2 -74.7 -79.1

68.0 68.8 83.1 84.5 91.0 93.0

21.56 -72.3 -70.0 -75.3 -74.9 -81.1 -85.3

65.1 65.8 77.6 81.8 84.6 86.8

22.03 -77.1 -70.6 -86.5

60.3 82.3 85.6

22.97 -71.6 -65.4 -77.8 -75.8 -79.6 -84.6

65.8 70.4 75.1 80.9 86.1 87.5

24.37 -83.5 -80.4 -79.1 -76.9 -83.3 -89.5

53.9 55.4 73.8 79.8 82.4 82.6

24.44 -79.5 -86.9 -88.1 -85.7 -92.0

56.3 66.0 68.6 80.0 80.1

25.25 79.0 -75.8 -80.4 -79.7 -84.7 -90.8

58.4 60.0 72.5 77.0 81.0 81.3

-26-
Table II continued

f(MHz) 2.00 1.618 0.520 0.412 0.182 0.121

d(km)

25.31 -81.5 -74.7 -84.4 -79.8 -82.7

55.9 61.1 68.-5 76.9 83.0

30.81 -82.5 -78.8 -80.7 -81.7 -82.2 -87.8

54.9 57.0 72.2 75.0 83.5 84.3

31.94 -76.0 -74.0 -80.3 -82.2 -81.7 -84.7

61.4 61.8 72.6 74.5 84.0 87.4

32.75 -87.4 -83.1 -88.6 -90.2 -89.5 -94.7

50.0 52.7 64.3 66.5 76.2 77.4

35.03 -73.9 -72.5 -88.9 -82.8 -82.9 -89.1

63.5 63.3 64.0 73.9 82.8 83.0

37.19 -78.2 -76.4 -91.6 -83.0 -82.9 -91.4

59.2 59.4 61.3 73.7 82.8 80.7

38 41 -77.7 -75.0 -87.3 -86.8 -89.4 -89.9

59.7 60.8 65.6 69.9 76.3 82.2

39.50 -80.6 -77.2 -91.1 -88.1 -91.8

56.8 58.6 61.8 77.6 80.3

40.87 -83.9 -81.0 -89.3 -91.1 -86.9 -87.3

53.5 54.8 63.6 65.6 78 8 84.8

43.16 -94.1 -85.4 -98.5 -90.8 -89.8 -94.2

43.3 50.4 54.4 65.9 75.9 77.9

43.69 -93.0 -88.3 -94.7 -91.4 -'92. 1 -97.3

44.4 47.5 58.2 65.3 73.6 74.8

44.31 -90.2 -85.2 -93.2 -92.9 -92.3 -93.7

47.2 50.6 59.7 63.8 73.4 78.4

44.78 -85.0 -94.0 -90.5 ~90.5 -92.4

50.8 58.9 '66.2 75.2 79.7

The figures show fairly good agreement between measurem~nts and WAGNER predictions ~t the two higher frequencies,

f = 2.00 and 1.618 MHz. At the lower frequencies, the agreement

is less satisfactory; however, many of the measurements still

fallon or very near the WAGNER curve.

Since the Canyonlands path crosses the Colorado River at

about 28 km, another run of WAGNER was made for f = 2 MHz

assuming cr = 0.1 Slm, E = 80 over this small portion of the

path. Figure 15 presents the comparison and shows only a very

slight improvement over the corresponding plot of Figure 9:

-27-
WAGNER was also run for f = 2 MHz using a fairly coarse file

of digitized topographic data we happen to have. Figure 16 shows

the "ECAC" profile and measurement/WAGNER comparisons for this run;

the agreement is less satisfactory as can be seen by comparing

with Figure 9.

San Francisco

The San Francisco path was 37 km along and provided 10

sites at which measurements were taken. All frequencies except

f = 2 MHz were recorded at every site. A tabulation of the

data is presented in Table III. The constants used to evaluate the DBU were determined from the measured power levels

recorded at the site at d = 27.04 km.

Table III. Measured received power in dB ,P (upper number),

and field strength in dB above 1 ~v/m, flBU(lower number) ,

for the designated frequencies and distances from the

transmitter along the San Francisco path.

f (MHz) 2.00 1.619 0.518 0.419 0.161 0.137

d(km)

11.45 -46.85 -42.97 -72.45 -77.08 -72.74 -74.54

96.0 98.1 93.0 97.1 95.8 97.0

18.98 -51.97 -47.90 -77.66 -83.81 -81.75 -83.93

90.9 93.2 8=7.8 90.4 86.8 87.6

20.31 -44.48 -91.03 -97.68 -90.24 -91.49

96.6 74.4 76.5 78.3 80.0

27.04 -55.97 -54.33 -79.62 -88.66 -83.39 -86.40

86.9 86.7 85.8 85.6 85.1 85.1

28.49 -63.01 -61.78 -90.87 -94.20 -100.93 -104.25

79.9 79.3 74.6 80.0 67.6 67.3

31.50 -55.42 -52.36 -86.51 -90.50 -93.68 -97.41

87.5 88.7 78.9 83.7 74.8 74.1

32.87 -61.97 -78.80 -86.72 -104.16 -106.07

79.1 86.7 87.5 64. 3 . 65.4

34.69 -67.09 -62.24 -84.99 -90.63 -88.92 -90.80

75.8 78.8 80.5 83.6 79.6 80.7

35.83 -71.74 -67.15 -87.52 -92.52 -86.63 -91.05

71.2 73.9 77.9 81.7 81.9 80.5

37.10 -66.74 -83.91 -89.23 -88.76 -91.29

74.3 81.5 85.0 79.7 80.2

-28-
Figures 17 through 22 show the measurements (X's)/WAGNER

comparison for the 6 frequencies, the lower portion of each

figure representing the terrain profile for the San Francisco

path. The box in the upper right corner of the field strength

plot indicates the ground constants used over the various segments of the path.

The comparisons show better agreement, again, at 2 MHz,

with the lower frequencies having more spread between measurement and prediction. Most of the measurement sites for this

path were necessarily located in heavily congested areas, and

the recorded signals may have been affected by interference

from nearby structures.

Santa Rita

On the Santa Rita Mountains path, measurements were taken

at 16 sites along a 23 km radial, with data at all 6 frequencies

being obtained at every site. The recorded data are shown in

Table IV. The constants used to adjust the DBU were determined from the first site at d = 2.48 km.

Table IV. Measured received power in dBm, P . (upper number),

and field strength in dB above 1 ~V/m, flBU(lower number),

for the designated frequencies and distances from the

transmitter along the Santa Rita path.

f(MHz) 2.00 1.619 0.518 0.419 0.160 0.137

d(km)

2.48 .-;37.65 -33.51 -61.92 -65.35 -58.62 -61.17

104.0 104.4 105.1 105.1 105.1 105.1

5.81 -50.05 44.65 -69.41 -71.60 -65.77 -67.67

91.6 93.3 97.6 98.8 98.0 98.6

6.92 -55.59 -49.54 -70.86 -74.65 -68.63 -69.86

86.1 88.4 96.2 95.8 95.1 96.4

8.39 -63.69 -58.93 -79.25 -79.66 ,-74.68 -75.64

78.0 79.0 87.8 90.8 89.1 90.7

9.46 -67.70 -61.91 79.99 -83.19 -77.77 -79.49

74.0 76.0 87.1 87.2 86.0 86.8

9.85 -61.09 -57.14 -72.13 -75.15 -69.13 -71.26

80.6 80.8 94.9 95.3 94.6 95.0

-29-
Table IV. Continued

f (MHz) 2.00 1.619 0.518 0.419 0.160 0.137

d(km)

10.19 -64.45 -59.54 -75.18 -76.52 -72.19 -75.35

77.2 78.4 91.9 93.9 91.6 91.0

11.41 -67.59 -62.54 -74.63 -77.91 -72.56 -73.59

74.1 75.4 92.4 92.5 91.2 92.7

12.30 -69.91 -66.47 -79.54 -81.04 -77.15 -79.92

71.8 71.5 87.5 89.4 86.6 86.4

13 02 -76.97 -71.54 -89.58 -92.29 -86.20 -87.24

64.7 66.4 77.5 78.1 77.6 79.1

13.35 -76.09 -70.07 -89.09 -89.76 -87.46 -89.73

65.6 67.9 78 0 80.7 76.3 76.6

13.70 -73.48 -66.72 -84.60 -87.07 -79.10 -84.17

68.2 71.2 82.5 83.3 84.7 82.1

14.77 -74.23 -68.41 -83.08 -88.44 -81.16 -82.16

67.5 69.5 84.0 82.0 82.6 84.1

16.82 -74.02 -68.16 -81.28 -82.02 -74.47 -76.78

67.7 69.8 85.8 88.4 89.3 89.5

22.42 -77.56 -71.19 -85.40 -86.78 -81.10 -81.45

64.1 66.8 81.7 83.6 82.7 84.9

22.84 -79.78 -71.80 -86.36 -87.37 -81.12 -81.90

61 9 66.2 80.7 83.0 82.6 84.4

WAGNER runs were made for two different sets of ground

constants, the only difference being in the length of the

"mountain" segment of the profile. One set assumed the

"mountain" constants, (J = 10- 5 Sim and E = 5, to extend from

7.2 km to 16.4 km; the other set had this segment extending

from 7.2 km to 12.95 km (see ground constant tables in the

figures).

Figures 23 to 36 show comparisons at the 6 frequencies

for the Santa Rita path; again, the terrain profile is shown in

the lower portion. of the figures. From comparisons of figures 23

and 24 it would appear that better agreement between measurements

and prediction is obtained if the low conductivity of the

mountainous material ends at about 13 km rather than 16 km. As

with the other paths, the higher frequencies show better measurement/prediction agreement than the lower frequencies. Figure 25

-30-
shows comparison of measurement prediction using measured values

for the conductivity (Kissick et al., 1978). The measured

conductivity for the peak near 10 km is much higher than that

given by Lytle (1974) for this type of granite rock. However,

Lytle's value corresponds to rock with all moisture absent and

the observed values by Kissick were under wet conditions. Kissick

may also have been observing the effect of the top or surface

soil. The values for the conductivity on either side of the peak

of the ridge observed by Kissick are larger than the sedimentary

values shown by Lytle, perhaps because the alluvial deposits

observed by Kissick were a result of erosion and not part of

actual strata. The results in Figure 25 motivated a simple two

section flat-earth model for the predictions shown in Figure 26.

The predictions show a "recovery effect" at about 16 km corresponding to the assumed jump in conductivity from .0005 s/m to

.005 s/m. Although the agreement" between predictions/measurement

is reasonable out to about 10 km, the agreement thereafter breaks

down, indicating in part the diffraction loss over the ridge needs

to be included in the predictions.

Nevada

Data were recorded at 22 sites for all 6 frequencies on

the Nevada path. The data are tabulated in Table V with the

constant~ used to adjust the DBU determined from the first

site at d = 1.90 km.

-31-
Table V. Measured received power in dBm, P (upper number),

and field strength in dB above 1 ~V/m,mDBU (lower number),

for the designated 'frequencies and distances from the

transmitter along the Nevada path.

2.38

d(km)

1.90

3.56

5.55

10.38

10.82

14.06

17.78

18.67

20.15

21.36

22.46

24.33

26.94

28.53

36.00

f(MHz) 2.000

-39.27

106.0

-41.13

104.2

-45.77

99.5

-65.0

80.3

-88.5

56.8

-81.0

64.3

-79.0

66.3

-80.0

65.3

-80.5

64.8

-80.0

65.3

-81.0

64.3

-83.0

62.3

-84.0

61.3

-84.0

61.3

-85.68

59.6

-83.75

61.5

1.619

-33.52

106.4

-35.55

104.4

-40.14

99.8

-55.0

85.0

-82.0

58.0

-76.0

64.0

-71.0

69.0

-73.5

66.5

-74.5

65.5

-74.0

66.0

-75.0

65.0

-77.0

63.0

-77.5

62.5

-77.0

63.0

-79.39

60.6

-78.14

61.8

0.518

-58.31

107.1

-58.44

107.0

-63.47

102.0

-71.0

94.5

-93.0

72.5

-84.0

81.5

-84.0

81.5

-83.5

82.0

-87.0

78.5

-87.0

78.5

-87.0

78.5

-87.0

78.5

-91.0

74.5

-89.0

76.5

-91.28

74.2

-91.38

74.1

-32-

0.419

-62.87

107.2

-63.04

107.1

-69.36

100.8

-77.0

93.1

-92.5

77.6

-86.0

84.1

-85.0

85.1

-87.0

83.1

-89.0

81.1

-89.5

80.6

-89.0

81.1

-91.0

79.1

-93.0

77.1

-92.0

78.1

-94.98

75.1

-96.08

74.0

0.160

-58.38

107.3

-57.72

107.9

-63.67

102. 0 '

-75.5

90.2

-82.0

83.7

-75.5

90.2

-75.0

90.7

-77.0

88.7

-78.5

87.2

-79.5

'86.2

-81.0

84.7

-80.0

85.7

-81.0

84.7

-81.0

84.7

-82.22

83.4

-85.40

80.3

0'.137

-60.38

107.3

-58.95

108.8

-67.75

100.0

-79.0

88.7

-85.0

82.7

-77.5

90.2

-78.0

89.7

-78.5

89.2

-82.0

85.7

-82.0

85.7

-84.0

83.7

~83.0

84.7

-84.0

83.7

-83.0

84.7

-85.47

82.2

-88.81

78.9
Table" V. Continued

f (MHz) 2.000 1.619 0.518 0.419 0.160 0.137

d(km)

36.32 -84.28 -78.44 -91.32 -96.42 -86.09 -89.50

61.0 61.5 74.1 73.7 79.6 78.2

39.53 -87.12 -80.38 -93.69 -97.07 -86.12 -90.53

58.2 59.6 71.8 73.0 79.5 77.2

45.22 -96.45 -88.21 -96.08 -98.52 -87.05 -90.98

48.8 51.7 69.4 71.6 78.6 76.7

47.75 -91.89 -85.96 -97.02 -99.40 -89.28 -90.71

53.4 54.0 68.4 70.7 76.4 77.0

50.36 -92.26 -85.41 -95.89 -98.42 -87.10 -90.45

53.0 54.5 69.6 71.7 78.6 77.3

52.46 -94.34 -87.72 -98.76 -99.40 -88.09 -91.57

51.0 52.2 66.7 70.7 77.6 76.1

WAGNER predictions for the 6 frequencies, together with

the measured data (X's), are shown in Figures 38 through 43.

Figure 37 is a comparison of the data at f = 2 MHz with the

field strength as calculated by Program INTEQ. In general, the'

data lie somewhat above the WAGNER predictions, but the trend of

the measurements and calculations are similar. It would appear

that a = 0.02 81m is not the correct value for the conductivity over the "plains" portions of the profile. A higher

value of a would raise the prediction curves and give much

better agreement with measurements.

-33-
Freq. (MHz) = 2.

12:1r----t----t----t---+-------.j

ZAOO

2200

_ 2000

5

...

.c

.~ 1800 Ql

.c

,coo

I

10

I

20

X(km)

I

SO

I

£0

Figure 9. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 2 MHz.

-34-
EPS

, Freq. (MHz) = 1.618

:l:r------r----~---_r_------~

m 1-- -+- .+ -+~.2lL._J~lL~..L.I

1201t-----+----4-----+----+------J

1200

I

10

I I

20 50

X(km)

I

40

Figure 10. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 1.618 MHz.

-35-
Freq. (MHz) = 0.520

OKII SIGIIA EPS

48.58 .004000 5.0

120tt----+----+----t----+----I

<, ICO

::l

a:l

"d

9C

8.

70

o.

5C

zeoo

2400

2200

2000

g

+J

.g, 1800 ....

Q)

.<::

ISOO

I

10

I

20

I

so

X(km)

Figure 11.

-

Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.520 MHz.

-36-
Freq. (MP.z) = 0.412

IlO,---,----,-----,- ---.

DKII SIGIlA EPS

l8.58 .00lOOO 5.0

mt----t-----t----+-----.--_-1

120 1t------t---+---f----t------1

<,

::l

a::l :00t-~,1r_t_---+----+---__+---l .'"(j

2AOO

2200

2000

+J

'§..1800

...

<lJ

.<:

1600

IAOO

1200

I

\0

I I

20 so

X(km)

I

lO l8.6

Figure 12. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.412 MHz.

-37-
Freq. (MHz) = 0.182

Dltll SIG!lA EPS

A8.58 .DDADOO 5.0

mt----i----+---+-----r---t

:zctt----i----+----+----+----I

2200

2000

5

.... 1800 .....

<l>

.c:

1200

10000 10

canyonlands

I I

20 SO

X(km)

AO AI.;

Figure 13. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.182 MHz.

-38-
Freq. (Illiz) = 0.121

:lOr---T----.----.-------~

01(11 SLGIlA EPS

l8.58 .00lOOO 5.0

I5Or---t----t----+----r----I

120tr---t----+----t----I----I

90i----t-l~!:::::--+__;_--+----+-----J

8:1---t----t-~::..---+--VC~rA-1t----1

100 i-r'r-t----+-'----+----+-----J

2100

2200

2000

§

.....

.g, 1800 .....

Q)

.c

1600

IlOO

1200

,

to

I

20 X (krn)

I

50

I

lO lB. 6

Figure 14. Path profile (lower portion) and received signal

(in dB above 1 jlV/m for 1 kW effective radiated

power) for Canyonlands, utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 0.121 MHz.

-39-
Freq. (MHz) 2.

1501-----t-----+-----I

01(11 SlGII4 EPS

26.82 .00lOOO 5.0

29.l0 .100000 80.0

l8.58 .00lOOO 5.0

120n----t----t-----l-----,~---l

1I011'r---+---+---+---+----1

IOOI-\-.;----t----+----+------4-----1 1\

90r---J~r-.+----+---+-----+-----J

80t---~1_---+----+-----1----J

1\

~j ~~ X

~VW

1

2100I2200 I1 I I

-

-

_ 2000 I-

.5

.....

.g, 1800 l- .....

OJ

.c

1600 I- .-J IlOOI-~

1200 I-

"

-

-

-

I

10

canyonlands

I I

20 50 X (km)

I

lO l8.6

Figure 15. Path profile (lower portion) and received signal

(in dB above 1 ~v/m for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 2 MHz.

-40-
EDS

Freq. (MHz) = 2.

1'0,---.----,----1"-'---------,

mt----+----+---+.-!!L..a.-.i~i.L~J.....J

1201r----t-----t----+----l-----.;

2'00

2200

2000

.....

'§, 1800 ....

Q)

.<::

1200

I

10

canyonlands

I I

20 50

X (krn)

C4NYOIl.AIllS Tl-Ill

I

'0 AB.'

Figure 16. Path profile (lower portion) and received signal

(in dB above 1 ~V/m-for 1 kW effective radiated

power) for Canyonlands, Utah, path. Crosses denote

measured 2.5 min. averages. Frequency = 2 MHz.

-41-
37.3 3. X (krn)

San Francisco

:

~K~ s:~~~ E~S

.23 .:3:::C :5. :

:1. ': 5" C::::C 8:. :

:2. :7 · =3:0~~ :5. ;

:B.72 5. J::COO B:. :

2:.3: .:3:CO~ :5. :

2s.94 5. =:::J: B:.:

2B.52 ·:3:::: :5. :

\ 3:.46 5. ~::::: B:.:

37.34 ·:3:::: :5. :

·

\

r-. x

: N-. _ 11

r-- , I

·

: x

· I . I ·

;1- -

;1- -

; .... -

".... J

.\t I II U I I /

: .. 2: ,

9

Freq. (11Hz) = 2. :4

..

• w

.....

Figure 17. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 2 MHz

-42-
37.3 3.

X (km )

Freq. (MHz) = 1.619

San Francisco

8

lC

Oltll SIGIlA EPS

.23 .000m 15.0

C n.u 5.0mco 8:.0

12.01 .030000 :5.0

t8.72 5.000000 81.0

20.31 .030000 15.0

0 2&.9l 5.000000 8U

28.52 .030000 !5.0

C \

3l.l9 5.000000 81.0

37.3l .030000 :5.:

c \

r-. X

X

X

j

r---MrlJ

: ~. I- A

vrvvW

X

:

, I ' I . I

c- -

;1- -

:1- -

'l- I

.

I

,

II Ll

2:

I \ I )

. V

9

.....

13

12

Figure 18. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 1.619 MHz.

-43-
37.3 3•

X(km)

San Francisco

OKH SIGH~ EPS

.23 .030000 \5.0

\1.4\ 5.000000 81.0

12.07 .030000 15.0

18.72 5.000000 81.0

20.31 .030000 15.0

2&.9£ 5.000000 8U

\

28.52 .030000. ~5. C

3U8 5.00::00 8:.0

37.3£ .030000 :5.0

\

<,

<:«

, ----r-J\-<: · X X

.. X

:

· I , I

· -

0- -

:- -

c~ - ,

0..-

J't J \ I J

0... ,. 2: . -

e

,.,.

to

50

: DC

120

Freq. (MHz) = 0.518

:~O

Figure 19. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 0.518 MHz.

-44-
37.5 3• X (krn)

(11HZ) = 0.419

·· DK" SIG"A EPS

.25 ."050000 15.0

· 11.41 5.000000 81.0

· 12.01 .050000 15.0

18.72 5.000000 81.0

20.51 .050000 15.0

0 2&.9£ 5.000000 81.0

28.52 .050000 15.0

\ 51.48 5.000000 81.0

5U£ .050000 15.0

0

0 \

<, x

0 v

r----1\.--.Jt. x LA'

0 ~'W

X

:

: I ' I -

:- -

·- -

:1- -

\

01-

I II U I \ I J .. 2: . San Francisco

8

9

It Freq.

:0

12

..

oW

5:

Figure 20. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 0.419 MHz.

45-
37.5 3.

x(km) San Francisco

Freq.(MHz) 0.161

·

o

8

0

O~Il SIGIlA EPS

· .23 .030000 15.0

· Il.£1 5.oeoooo 81.0

12.07 .030000 15.0

!8.72 5.000000 81.0

:\

20.51 .mooo 15.0

2&.9£ 5.oeoooo 81.0

28.52 .030000 15.0

51.£8 5.000000 81.0

•

\ 57.5£ .030000 15.0

:

X

:

----r-t\

: - ~- --.;-

X

:

X

X

:

I , I I -

I- -

- -

I- - ,

II II \t U , I } .. 2:

9

,.- -..

5"..

Figure 21. Path profile (lower portion) and received signal

(in dB above 1 ~v/m for 1 kW effective radiated

power) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 0.161 MHz.

-46-
37.3 3• X(l':rn) San Francisco

Freq. (MHz) = 0.137

0

01(11 SIGMA EPS

.23 .030000 15.0

0 It. oil 5.000000 81.0

12.07 .030000 15.0

18.72 5.000000 81.0

:\

20.31 .030000 15.0

2&.9£ 5.000000 81.0

28.52 .030000 15.0

3U8 5.000000 81.0

\ 37.3£ .030000 15.0

0

x

r--. c

r-- --1\ r---

0 ~~

- x

:

x

x

, I , r w I -

01- -

,... -

I- -

l-

..

I II JU

2:

I )V

8

.

"w..

9

'0

12

:3

Figure 22. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for San Francisco, California, path.

Crosses denote measured 2.5 min. averages.

Frequency = 0.137 MHz.

-47-
Freq. (MHz) = 2.

20 30.0 X(km)

01(11 SIGI1A EPS

7.20 .020000 10.0

16.l0 .000010 5.0

50.00 .020000 10.0

\

\

<,

X\

X) fN, X

~l rr'x--X r---.-

"',w-I

I

01- -

01- -

:~ -

-

0 I I SO o 10

Santa Rita Mtns.

100

250

120

IlO

9:

5

500

150

110

5 200

.....

.c:

'"

...

<l>

.c: ISO

Figure 23. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 2 MHz.

-48-
Freq. (MHz) = 2.

20 50.0

X(km)

:

:lr.~ S:G~A EPS

7.2: • C2~CCO ., , Illow

i2.95 1'\........ , ..

, .1lr1ltJ\IIlfl/ 5. :

3~. ~~ . C2:~J: to 0,ill."

:

.\

:! \, I I

J

I i

I i I I

~. --

X) ftl

X ; ~L.A ..

\(~ III X 1't'IJ

X

0 I I

01- -

O~ -

o~ -

Olr- -

0 I I 50 o 10

Santa Rita ~tns.

100

250

&

500

:l

:3

:2

..

<,

::s

CCl

-o ..

Figure 24. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 2 MHz.

-49-
01(1'1 SIGI'1" EPS

2.,(8 .005000 15.0

5.81 .005000 15.0

&.92 .00&500 15.0

8.59 .007500 15.0

\ 9.,(& .007200 15.0

12.50 .00&800 15.0

\. 15.02 .005&00 15.;

15.55 .OOG,(OO 15.0

-- 15.70 .007500 15.0

\ :l.7-: • OOGI 00 15.0

1&.92 .00550C 15.,0

. l(

. -.- 22.,(2 .007100 15.0 '\ ---- _.-----

5:. C: .00720= 15.0

: ~-~ -'---' .--.---,,- -r--'---- - -r----'-

l(~

l(

------ \l( .. l(

~. l(

l(

: f--

Y"\J

r----.. 0---

..

9

9

:cc

110

120

150

:.tc

10 15 20 25 50

X(km)

Santa Rita Freq. (MHz) 2.0

Figure 25. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 2 MHz.

-50-
50

100

110

90

80

<,

::J

CD 70

"0

60

F= 2.00 MHz

, DKM SIGMA EPS

1

16.00 0.0005 15.0 U 30.00 0.0050 15.0

X

~\X

\

X

-,

X

X~' X

X"'rK X I

Xx X

. X

X

5 10 15 20

Distance (krn)

25 30

Figure 26. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 2 MHz.

-51-
20 50.0 X(km}

DK'l SIG'lA EPS

7.20 .020000 10.0

16.l0 .000010 5.0

50.00 .020000 10.0

\

\ ~'0

X~

~"\j

xIW~

x x . . kL( r---..

0

0 I I

01- -

01- -

'~ -

- ofr._ -

0 I I 50 o 10

Santa Rita !Itns.

100

150

250

IlO Freq. (MHz) = 1.619

120

60

70

80

!5

500

150

110

200 ...,

.c

t7'

..,

(l)

.c

Figure 27. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 1. 619 MHz.

-52-
Freq. (!1Hz) = 1.619

o¥.~ SIG"~ EPS

7.20 • ~2~aCO 10.0

:2.95 • =JOO:~ 5.:

!:. == . 0200~O .. , -_."

;

.\.

. \

~10 ,

x~

x,,\

xr#1

: xlv.\~~ "

\1X r--- I

b I I

01- -

m... -

001- -.r ...

00I.- -

00 I I 5

!0

250

:2

.. :s:

<,

::s .. l!l

'0

10

Santa Rita I!tns. X(km)

20 30.0

Figure 28. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 1. 619 MHz.

-53-
20 50.0

X(km)

500

o 10

Santa Rita Htns.

1000

90

0

Ottll 51'"4 EP5

7.20 .020000 10.0

0 lS."O •000010 5.0

50.00 .020000 to.O

0

o \

\

\ x

x

M x I

X

J("

ILrr-- -

T I

f- -

... -

v- -

-

I I

1500

2500

1" Freq. (MHz) = 0.518

SO

5000

2000

.c'"0'.

.....

Q)

.c

12

15

Figure 29. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency =

0.518 MHZ.

-54-
Freq. (MHZ) ='1.518

20 30.0

x(km) o 10

Santa Rita 1!tns.

OK~ SIGMA EPS

7.20 .020000 : 0.0

:2.95 .000010 5.0

3UO .020000 10.0

.,

.\

: \

'\ x

:

X~ x

x

Mx Xv :

V"I,r Y'\J '---

00 I

00- -

OH- -

00 -

000 ..

500 I I

9

E20 .....

.c

'"

.....

OJ

.c 15

:2

8:

..!<:

<, .. ::l

a:l

-o ..

Figure 30. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 0.518 MHz.

-55-
20 50.0

x(km) o 10

Santa Rita Mtns.

DIt" 5IG"" EP5

7.20 .020000 10.0

0

16.l0 .000010 5.0

30.00 .020000 10.0

0

0\

,\

1\. x

0

'~ "II: X

M: Xx

0

V --....

70

00 I I

00 f- -

00 -

00 f- -..-r -

00 -

500 I I

10

25

13

12

Freq. (MHz) = 0.419

IlO

50

e

9

+J

.c

lJ'

.,..

OJ

.c 15

Ei 20

Figure 31. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 0.419 MHz.

-56-
20 30.0 X (km)

C 10

Santa Rita ri.tns.

.. ._ .

O~M SIGMA EPS

7.20 .020000 10.0

12.95 .ooom 5.0

0 30.00 .020000 IC. 0

0

,\

c \

~\ x

;

.~ x

VV\ y~ Xx , • II. . \f' r---- - '00 I I

00"- -

000 f- -

500 f- ....,.,.., -

COC -

500 I I

e

25

9

30

Freq (11T'z) = O. 1 9

:lO

13

12

3= " <, "

tl:l

"d

:0

Figure 32. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path Crosses

denote measured 2.5 min. averages. Frequency = o. 419 ~4Hz.

-57-
20 $0.0

x tkm)

Freq. (11Hz) = 0.160

50 o 10

Santa Rita Mtns.

80

100

0

OIVI SIGII~ [PS

7.20 .020000 10.0

0 1&.40 .000010 5.0

So.oO .020000 10.0

0

o \

,\

1\

-, - •

-K-.... 1 lOl

\ ....I'-V"'" -- - 0 I I

01- -

01- -

:~- -

-,

-

0

I I

90

150

12

250

10

~o

$00

IS

E200 ...,

.c

tl'

....

OJ

.c

Figure 33. Path profile (lower portion) and received signal

(in dB above 1 ~v/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 0.160 MHz.

-58-
20 30.0

X(km)

SOO o 10

Santa Rita Htns.

ee

0

CKI1 SIGI1A EPS

7.20 ,020000 tO,O

0

12.95 ,000010 5,0

30,00 ,020000 10,0

0

, \

'\

:

1\ x

X'"

~~

x ... """'"-.!!

\ --- I

,.. -:

I- -

.~ ----l

-

I I

1000

150

2500

Freo. (~'Hz) = 0.160

14

£ 2000 +J

.c

'"

....

OJ

.c

,.

.,

12

13

Figure 34. Path profile (lower portion) and received signal

(in dB above 1 llV/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 0.160 MHz.

-59-
20 50.0

X(kro)

0

OK" 51G"A £1'5

7.20 • 020000 10.0

0 IS.AO .000010 '5.0

50.00 .020000 10.0

0

0 \

0 \

l(

0

~~ l(l(

rv --.

l( r0 I I

0- -

0- -

:~ -

-

o. I I SO

o 10

Santa Rita Iltns.

100

250

12

jA Freq. (MHz) = 0.137

80

10

70

500

IS

Em....

.c:

t:'

....

Q)

.c: ISO

Figure 35. Path profile (lower portion) and received signal

(in dB above 1 ~v/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency = 0.137 MHz.

-60-
20 50.0 x (!':I'\)

Freq. (tlHz) = 0.137

50 o 10

Santa Rita Htns.

80

C

O~1l SIG'lA EPS

7.20 .020000 10.0

0

12.95 .000010 5.0

50.00 .020000 10.0

0

0\

,\

1\ x ,

, "'\

Xi',:

•

Xx

"""'"r'-- •

X - .

'0 f

0'- ; -

0'- -

:V -

"--'l

-

0 I I

!CO

12

250

9

.

50'0

15

:s 200

..,

.c

'"

....

<lJ

.c !SO

Figure 36. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Santa Ritas, Arizona, path. Crosses

denote measured 2.5 min. averages. Frequency =

0.137 MHz.

-61-
3• 52.5

x(km)

... 2.

Nevada

5

5"u

:

;\ :Il:~ S:G~~ E~S

5.8~ . 02~oa • 11.1/

\ - I J. :5 · :~oo: e.:

£5.00 · :200~~ 5~.

££.55 .~0010~ l~. 0

0 "l

52.£6 · 0'0"'0 I~. 0

:

0 'l~v

:

\ Xx "11~ 0

"IV ILx X II(

k :---- ---1, x X

l

II

: -

I I I I

- -

- -

I- -

I- -

-

I- ......

- -

I I I I

, ,

8

9

..,.,. •• /tI1i

Freq. (MHz) = 2.

:2

I''''

.... "''''

Figure 37. Path profile (lower portion) and received signal

(in dB above 1 ~v/m for 1 kW effective radiated

power) for Dry Lake, Nevada, path. Crosses denote

measured 2.5 min. averages. Frequency = 2 MHz.

Predictions made using PROGRAM INTEQ.

-62-
Freq. (MHz) = 2.

3. 52.5 XCkm)2.

Nevada

::.:~ 5'-'" .\J...... E?S

. 3.8: .:2:::: ... "

::. :5 ............ 8. : .,) .• _.. ,.

"3. :: .:2:::: 3:, :

: U.35 .... ,...".. ,- ." ........ , ....

\ 52. "0 .:2J::: ,-

.....

:

\

li

:

1I~ ~x X llr

1M- x

x x

I( .

I

-- I

: I I I I

f- -

-f- -

f- -

r- -

f- -

- .",.

I- -

I I I I

- ,- - 5"

..

8:

''''''f' ,will.

:2

350 ..

Figure 38. Path profile (lower portion)

(in dB above 1 ~v/m for 1 kW

power) for Dry Lake, Nevada,

measured 2.5 min. averages.

and received signal

effective radiated

path. Crosses denote

Frequency = 2 MHz.

-63-
52.5 3:

X(km)

2. ,.

.. Nevada

Freq. (MHz) ; 1.619

;

CKX SW~~. EPS

=

3.80 . =20~~: "''-oJ

to.:S · jJO~! = 8. :

t3. co .02COOj 3;. :

tt.35 · o:~ lOj . " ..... 52.to · :2JO~C 0 •• 01

\

;

\"'I

¥V1

.

\~ I~x Y.4 ..JW X y lk

,~ x x

: II

. I I I I

,... -

I- -

-

- -

- -

-=l

- -

I I I I -

o"

5

8:

:3

:1

5"

...,

.g, 25: 0 ....

.c'"

Figure 39. Path profile (lower portion)

(in dB above 1 ~V/m for 1 kW

power) for Dry Lake, Nevada,

measured 2.5 min. averages.

and received signal

effective radiated

path. Crosses denote

Frequency = 1.619 MHz.

-64-
52.5 3;

X(km)

2.

Nevada

....

Freq. (MHz) = 0.518

5:

: .- :K~ S:G~j. EPS

3.e~ . =2CC~~ .... :0. :5 ~:'II'J\' 11 • =.Jolt/.W e. :

43.j~ · ~2~C~~ 3:. :

4'.35 ·:00:=~ " . 5? l~ .1,n~'" ...

\

\

~~flY

X X X

I~ X XX

A X

'~ :«

- x

i; x ,

-'

: I I I I

.- -

"I- -

01- -

'- -

0 -

;- .A..-__. "::j

:'- -

:

I I I I

8:

:sc

.... M"""

Figure 40. Path profile (lower portion)

(in dB above 1 ~V/m for 1 kW

power) for Dry Lake, Nevada,

measured 2.5 min. averages.

and received signal

effective radiated

path. Crosses denote

Frequency = 0.518 MHz.

-65-
2• 3• 52.5

Freq. (MHz) = 0.419

5..'"

:::c

9

l:

:/l:X S:G!'!A E~S

3.8: . :2C=~~ " . 3:

.".

C. !5 .:0=01': 8. :

l3. ':: . J20:~: 3:. :

ll.35 .OOOlOO fA ..

: 5' l~ ~,nn"

."."

" .

: l

: \

. \

\ X X

X

X X

llw J /' X

WI' '--

~X y X

Iv- - : I I I I

:- -

;- -

;1- -

I- -

I- -

I- -=l

I- -

I I I I

. .. . .

2..' ",

35;

Nevada X(km)

Figure 41. Path profile (lower portion)

(in dB above 1 ~v/m for 1 kW

power) for Dry Lake, Nevada,

measured 2.5 min. averages.

and received signal

effective radiated

path. Crosses denote

Frequency = 0.419 MHz.

-66-
Freq.- (11Hz) = 0.160 R' :.C

:K!"! SIG1\~ EPS

3.e: . ~2000~ :0.0

. tc. :5 .OOOO!O u

l3. CO .020000 30.0

l4.35 .000100 : O. :

52.ll; .020000 I'" 'I ••• W

:

. \

\

\ v y

\~ x

x

XX X X 0 _____ X

.. v

."'"'---- "'I X X I--

'l X

. -

9

:3

:2

:s: .."

<,

::l

m

'lJ ..

4500 ..-----·.,------,-----,,...---1-·----,

... '''.'''' ,,11I'

2..' · ',

:::c

52.5

X(km)

2: ,.

.. 5:0L_--...L----..L-----::----~------!

Nevada

Figure 42. Path profile (lower portion)

(in dB above 1 ~V/m for 1 kW

power) for Dry Lake, Nevada,

measured 2.5 min. averages.

and received signal

effective radiated

path. Crosses denote

Frequency = 0.160 MHz.

-67-
Freq. (llHz) = 0.137

:~~ s:;;~:. EPS

3.8: . ;2~j~; ,01 ••

::. :5 .."..... , .. .lIw"J.w 8. :

L3.:: .n:::: 3:. :

LL.35 .J:C::: ".....

52.Lo .m,:: ., .

\

; \ -

: \ I.

X

\A X ... XX X X ''----. h.I. X

-- r----~ I , X

--t X

I -

9

4S::.------,-----,.----r----,------,

Nevada

,-

.. I

2:

I

3:

X(km)

I

4- 52.5

H'iaure 43. Path profile (lower portion)

(in dB above 1 ~V/m for 1 kW

power) for Dry Lake, Nevada,

measured 2.5 min. averages.

and received signal

effective radiated

path. Crosses denote

Frequency = 0.137 MHz.

-68-
Colorado Mountains

A study of the Colorado Mountain Data report (Johnson et

al., 1967) was made to find paths for measurement/prediction

comparison purposes. Only one radial has been found for which

data at all frequencies (f = 20, 50, and 100 MHz) and all five

sites are available. The sites (at 5, 10, 20, 30, and 50 km

from the transmitter) fall more-or-less along the radial, and

this is probably the best path for study. Other paths will have

much fewer comparison points.

The predictions/comparisons for one radial using both

PROGRAM WAGNER and PROGRAM INTEQ (~ufford's (1952) integral

equation) are shown in Figures 44 through 49. Both integral

solutions failed to yield convergent solutions at spacing intervals of 100 m and 50 m, as shown in Figures 44, 45, 47, and 48.

This particular terrain profile probably represents an extreme

in terms of roughness; however, the large amount of computer

time required (9~3 sec in the case of WAGNER) to go just 6 km

suggests more research on the problem is required.

5. SPACING/TIMING COMPARISON FOR PROGRAMS WAGNER

AND INTEQ.

Four spacings (100 m, 200 ro, 500 m, and 1 km) and 2 frequencies (137 kHz and 2 MHz) were evaluated using WAGNER and

INTEQ for the Nevada path previously discussed. The results at

2 MHz using WAGNER are shown in figures 50, 51, 52, and 53, and

using INTEQ in Figures 54, 55, 56, and 57. The results seem to

indicate that at the 100 m spacing WAGNER came close to the

measured values than INTEQ. There was also a smaller change

going from the 200 m spacing to the 100 m spacing using WAGNER

than for the corresponding spacing using INTEQ. However, INTEQ

was much faster; i.e., 100 m spacing using INTEQ took 7.60 sec

whi Le the 10 a m spacing using WAGNER took 76 .s

~--

ec . A 10 0 m

spacing at 2 MHz is 3 points every 2 radio wavelengths.

-69-
Freq. (MHz) = 20.080

1.1°,---1---.,------,-----..:.--------.

DI('I SIGII~ EllS

50.46 .008000 10.0

:20r-- - - -t-- - - -f-- - - -t-- - - ""T""- - - --J

:oor---t-------j~-----t-----+------l

.l0r-- - --IH-- - -4- - - -t- - - -+- - - UJ

20r-.....:----I~---i-----+----+---J

, .. ,.'" "'''''.

:5::

Colorado !ltns.

I I

20 30

x(km)

I

1,; 5:.5

Figure 44. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Colorado r10untain path. Crosses denote

measured median. Predictions using PROGRAM WAGNER,

100 m spacing intervals. At 20 km, the two

measured values correspond to two sites close to

the radial selected for comparisons.

-70-
20 30 50.5 X (kro)

10

Colorado Htns.

Freq. (MHz) = 20.080

0

D~II SIGIIA EPS

50.16 .008000 10.0

0

\

\ ._._-. ._--

II ~} ~, I . N\ J\ I

HI ~\J

~\J V.l

------ - --

1

c -r I I I

I- -

- -

-

I-

~~~ / -

-

I- -

I I I I

rsee

2~

20::

100

25::

12

#""" "<101_

5ww"

l5::

'8 35::

+J

.c

.S' 3~C~ OJ

.c

Figure 45. Path profile (lower portion) and received signal

(in dB above 1 ~v/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM WAGNER.

-71-
20 50 5:.5

x(km)

.0

Freq. (l\I:z) = 20.084

2

0

l)l(H 51101I4 EP5

S.OO .008000 10.0

0

0

C

0 ---------- \0 I "-'_.,._------

:

:

,

.

• I I r I

:1- -

:1- -

:1- -

:1-

:1- -

:1- -

Cl- -

I I I I

, ,

Co Lo r a'do Mtns.

ISC

25:

10

''''''f' ... 11.

12

IS

,.,

.."

5..

"

Figure 46. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM WAGNER.

-72-
20 50 S:.5 X (krn)

! 0

Colorado !1tns.

Freq. (MHz) = 20.084

0

01111 SlGll4 EPS

0 50.A& .008000 \0.0

0

\ 0

\

0

~\ 0

0 \

I

0 '4 V~ II

~VJ' 0

0

0

. I , I I I

:f- -

:f- -

~f- -

Of-

:f- -

:f- -

:f- -

: I I I I

2

7

5

8

9

10

S"..

.IS:

01".. S 35: +'

.<:

t1'

.....

Q) 5" .<: ..

2S0

20:

:SC

.., ...

Figure 47. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM INTEQ.

-73-
20 30 5U

X(km)

10

Colorado r~tns.

DIll! SlGll4 EPS

50.l. .008000 10.0

\

\

II \ A

0

lVV •

0

n~

0

0

I T I I

I- -

r-- -

- -

...

- -

- -

-

I I I I

2

70

80

90

:50:

25::

20::

100

Fren. (M~'z) 20.084

110

5... """

C 35::

Figure 48. Path profile (lower portion) and received signal

(in dB above 1 ~V/m for 1 kW effective radiated

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM INTEQ.

-74-
5~. 5 20 30

X(km)

.0

Colorado Mtns.

Freq. (MHz) = 20.084

0

Cltll SIGI\4 EPS

!IO.lS .008000 10.0

0

0

o \'

0

0

C

: I I I I

;1-- -

;1- -

:1-

-

- -

I I I I , .

2

II

12

10

rse:

'''f'I'' '_"'111

,.,

....

5.."

Figure 49. Path profile (lower portion) and received signal

(in dB above 1 VV/m for 1 kW effective radiated·

power) for Colorado Mountain path. Crosses denote

measured median. Predictions using PROGRAM INTEQ.

-75-
5 10

\

\ "

1\\

· \ -- •

N\ · -_. .- •

'\ -_.._-- \ •

\~lC lC\

0: _.._.

-

...

9

,.. • • tI

120

5 10 15

\

v~· l(

II.

V\ 11'\

l/

)(

x

0- I 5

o

70

90

80

120

110

100

X (km)

t.x = 1000J'Y1

X (krn)

t.x = 500m

Nevada Freq. (MHz) = 2.0 Nevada Freq. (MHz) 2.0

Figure 50. Nevada path at Figure 51.

2 MHz using PROGRAM

WAGNER with 1 krn

spacing of observation points.

Nevada path at

2 MHz using PROGRAM

WAGNER with 500 rn

spacing of observation points.

-76-
\

\ I\~

_. -.- ------ ~._._.

J

.- -

1 ~."J i/V --

·

•

· .- • : 0

...

..

I 10

lCO

120

5 to 15

\

\

1\'

J\

I

\

(~l(

---~-

l(

--

...

• Ii

150

8:

120

I 10

loe

X (km)

f:.x = 200m

X(km)

f:.x = 100m

Nevada Freq. (MHz) = 2.0 Nevada Freq. (MHz) = 2.0

Figure 52. Nevada path at Figure 53.

2 MHz using PROGRAM

WAGNER with 200 m

spacing of observation points.

Nevada path at

2 MHz using PROGRAM

WAGNER with 100 m

spacing of observation points.

-77-
Nevada Freq. (HHz) 2.0

50

0 5 to :5

X(km)

t:,.x = 500m

Nevada Freq. (MHz) = 2.0

110

)(

)(

I",,~• ~~ I \ I

II

90 - ._- --- I

\J:

e=

<,

:;j

a:I

"(j ...

.

10 tS

X(km)

t:,.x = 1000m

)(

x

'~ i

I

I

l

~I

-------

I(

I(

,

I

Ie I

I

!

,

I

70

eo

50

o

90

so

itO

100

Figure 54. Nevada path at Figure 55.

2 MHz using PROGRAM

INTEQ with 1 km

spacing of observation points.

Nevada path at

2 MHz using PROGRAM

INTEQ with 500 m

spacing of observation points

-78-
5 10 15

\

\

\"I

"--

Ii

f'

-"

)(

&0

70

50

o

90

110

120

100

5 10 15

\

"I

~IrY

,

I

X

70

50

o

90

110

120

100

X(km)

Lx = 200m

Nev5.da

Nevada Freq. (MHz) = 2.0

Figure 56. Nevada path at Figure 57.

2 MHz using PROGRAM

INTEQ with 200 m

spacing of observation points.

X(km)

Lx = 100m

Freq. (MHz) = 2.0

Nevada path at

2 MHz using PROGRAM

INTEQ with 100 m

spacing of observation points.

-79-
At 137 kHz the results in Figures 58, 59, 60, 61, 62, 63, 64, and

65 indicate that both WAGNER and INTEQ have converged using the

500 m spacing, which is nearly three points per wavelength. A

conservative estimate for the spacing of points regardless of

terrain profile, even for the Colorado Mountain example, might

be

Observation

interval

spacing, ~x 1/3 wavelength

6. CONCLUDING REMARKS

Nine examples of measurement/calculation comparison discussed in the previous sections partially verify the applicability

of PROGRAMS WAGNER or INTEQ for estimating ground wave propagation over irregular terrain. The predictions appear to follow

the general trend of the data except for regions near the transmitter and for large path distances. Further comparisons with

other data are obviously needed before the method is completely

validated. However, to the authors' knowledge, no other method

attempting a detailed prediction for this complex problem has

been published. It is hoped that the method presented here will

at least partially fulfill the need for a better prediction of

propagation effects in telecommunication systems.

Extensions of the model to include off-path terrain effects

(the three-dimensional ground wave problem) are planned for the

future. A full wave treatment would also provide more accurate

estimates of the field, especially in those regions where complex

interference phenomena are encountered. Wait (1974) has pointed

to the use of alternative methods for evaluating propagation over

irregular terrain in cases where the terrain can be considered

a single knife-edge or a combination of several knife-like discontinuities, and his approach should be considered, especially

when the behaviour of the field in the vicinity of a single

terrain feature is desired.

-80-
10 15

)(

\

\

'\

1\ 'Oi

II;

)(

\

-

85

110

115

IC5

120

100

10 15

\

\

\

)(

\

\

---

\1\

. -_.. \ )/

.

\

II;

x

5 _._----- f-.

l

0-

e

100

9

105

110

115

X(km)

t::.x = 1000m

X (km)

t::.x = 500m

Nevada Freq. (MHz) = 0.137

Figure 58. Nevada path at

137 MHz using

PROGRAM WAGNER

with 1 km spacing

of observation

points.

Nevada Freq. (MHz) = 0.137

Figure 59. Nevada path at

137 MHz using

PROGRAM WAGNER

with 500 m spacing

of observation

points.

-81-
\

x

\

" l( lI;

V -\-",""

-

- -- ~.

l(

-- --

~\

I~ ...- .- '"

x "

l~ ... , J'

- -_.-

5 15

I:

... ...

:2~

5 10 15

90

150

110

:20

X(km)

/:,X = 200m

X(km)

/:'x = 100m

Nevada

Figure 60.

Freq. (MHz) = 0.137

Nevada path at

137 MHz using

PROGRAM WAGNER

with 200 m spacing

of observation

points.

Nevada Freq. (MHz) = 0.137

Figure 61. Nevada path at

137 MHz using

PROGRAM WAGNER

with 100 m spacing

of observation

points.

-82-
5 10 15

x

X

1\ I "

Y

X

\

r-;

90

95

80

o

85

110

105

100

5 10 16

l(

x

\ "

\

x

l(

\

80

o

90

95

85

100

105

110

X(km)

/:::'x = 1000m

X(km)

/:::'x = SOOm

Nevada Freg. (HHz) = O. 13 7 Nevada Freg. (HHz) = 0.137

Figure 62. Nevada path at

137 11Hz using

PROGRAM INTEQ

with 1 krn spacing

of observation

points.

Figure 63. Nevada path at

137 MHz using

PROGRAM INTEQ·

with 500 rn spacing

of observation

points.

-83-
5 10 15

...---- )(

- ----_...f--. ......._.

_.- (_.- ___ . 0.- ..

---- - >I

T

l(

... _.- _.•- .. \

II •

v,. -..J

80

o

90

85

120

115

I 10

100

105

5 10 15

\

)(

\

\

\ . >I

It

)(

V~ 80

o

85

90

100

105

ltO

115

X(km)

lIx = 200m

X(km)

lIx = 100m

Nevada Freq. (MHz) = 0.137 Nevada Freq. (HHz) 0.137

Figure 64. Nevada path at Figure 65.

137 MHz using

PROGRAM INTEQ

with 200 m spacing

of observation

points.

Nevada path at

137 MHz using

PROGRAM INTEQ

with 100 m spacing

of observation

points.

-84-
7. ACKNOWLEDGEMENT

The Electromagnetic Compatibility Analysis Center (ECAC)

supported the research described in this paper. Ms. Jacqueline

R. Janoski, Mr. J. A. Zoellner, and Dr. R. A. Whiteman of ECAC

initiated the idea to provide ECAC with an up-to-date, efficient

prediction algorithm for propagation over irregular, inhomogeneous terrain. Mr. Mark Weissberger of ECAC made many helpful

suggestions during the course of the research. Mrs. Rita

Reasoner of ITS provided invaluable computer programming

assistance. Also, the work was supported in part by the Department of the Air Force, Space and .Missile Systems Organization,

Norton Air Force Base under the sponsorship of Captains Bob

Barrell and Bob Barberg and technical direction from TRW staff

and by Mr. J. Cullhane, Dr. Leo Baggerely, and Mr. Jim Wolcott.

8. REFERENCES

Abramowitz, M. and I. A. Stegun (1964), Handbook of Mathematical

Functions, National Bureau of Standards, AMS 55, Ch. 7.

CBS Radio (1971), Field intensity measurements to establish

performance of directional antenna station KCBS, San

Francisco, California, Report E 70704-A; CBS Radio, Columbia

Broadcasting System, Inc.

Hansen, P. (1977), Measurements of basic transmission loss for

HF ground wave propagation over seawater, Radio Science,

12, No.3, pp. 397-404, May-June.

Head, H. T. (1958), Field strength measurement survey for Association of Maximum Service Telecasters, Inc., Buffalo, New

York; A.D. Ring and Associates, Washington, D. C.

Heckscher, J~ (1979), RADC Technical Report, to be published.

Hopkins, M. (1977), ECAC-HDBK-77-07, ECAC's topographic data

handbook, IITRI, Annapolis, Md., April; or ECAC's topogr~phic

data users manual, ECAC-UM-77-013.

-85-
Hufford, G. A. (1952), An integral equation approach to the

problem of wave propagation over an irregular terrain,

Quart. J. Appl. Math., 9, pp. 391-404.

Johnson, M. E., M. J. Miles, P. L. McQuate, and A. p~ Barsis

(1967), Tabulcations of VHF propagation data obtained over

irregular terrain at 20, 50 and 100 MHz, Part II: Colorado

MountainSl ESSA Tech. Report No.: IER 38-ITSA 38-2, u. S.

Department of Commerce, Environmental Sciences Services

Adnu.nLst.ra t i.on , Institute for Teleconununication Sciences,

Boulder, CO B0303.

Kissick, W. A., E. J. Haakinson, and G. H. Stonehocker (1978),

Measurements of LF and MF radio propagation over irregular,

inhomogeneous terrain, NTIA Report No. 78-12, Boulder,

CoLozado 80303.

Lytle, R. J. (1974), Measurement of earth medium electrical characteristics: Techniques, results and applications, IEEE

Trans. GeoScience and Electronics, GS12, pp. 81-101.

Monteath, G. D. (1973), Applications of the Electromagnetic

Reciprocity Principle, (Pergamon Press, New York), p. 116.

Ott, R H. (1970), An alternative integral equation for propagation over irregular terrain, Radio Sci. ~, No.

pp. 767-771, May.

Ott, R. H. (1971a-), An alternative integral equation for ~)ropagation over irregular terrain, 2, Radio Sci., ~, No.4,

pp • 4 29- 43 5 •

Ott, R. H. (1971b), A new method for predicting HF ground wave

attenuation over inhomogeneous, irregular terrain, u. s.

Dept. 'of Commerce, Res. Rept. No. OT/TRER 7, Jan. (NTIS

Access No. AB721179).

Ott, R. H. (1974), Fock currents for concave surfaces, IEEE Tran .

Ant. Prop. , Al?-:-2£, No. 2, Mar ch , pp. 357-360.

Wait, J. R. (1974), Recent analytical investigations of electromagnetic ground wave propagation over inhomogeneous earth

models, Proc. IEEE 62, No.8, Aug., pp. 1061-1072.

-86-
APPENDIX A: Effective Surface Impedance for a Two-Layered Ground.

The effective surface impedance, 6, appearing in Program

WAGNER can be modified to account for the effects of stratified

layers in the ground as discussed in King and Wait (1976). We

will denote the relative (complex and anisotiopic) permittivity

and permeability by E(=E -i60Ao) and~. Furthermore, assuming r

propagation in the x-direction and the positive z-axis in the

vertical downward direction, the subscripts, x, y, z, attached

to a quantity will refer to that quantity in the x, y, or z

directions; the subscripts, 1, 2, 3, etc., refer to layer 1 (the

top layer), layer 2, layer 3, etc.

For now, it will be assumed that only two layers are present: a surface layer of height h, and a lower layer of infinite

extent downward. With denoting the angle of incidence of the

wave with the ground surface, the effective surface impedance

for a vertically polarized wave is given by

K2 + Kltanh(ulhl) 6(~) = Zl (~)/no' Zl (~) = Kl ~+ K

2tanh(ulhl) ,

where Kl = (n o/E

x l) J0y l EXl - (EXl/Ezl)cos2~

K2 = (n O/E

x 2) iGy 2EX2 - (EX2/Ez2)COS2~

u l = ik ;G~lExl - ( EXl/Ezl)cos2~

and n = 000I~ /E 120TI ohms, k = 2TI/A .

The sign of u l is chosen such that the field goes to zero at

very large distances.

For horizontal polarization, 6(~) is obtained by interchanging and E in the preceding equations. Thus,

-87-
I 2 where NI = (l/nollx l) /]1Xl 'vi - (llxl/llzl)cOS ljJ

t 2 N2 = (l/no llx2) l]1x2£Y2 - (llx2/11z2)cOS 1/J

+ ik hX1£Yl - 2

vI = (llxl/llzl)cOS 1/J

Reference

King, R. J., and J. R. Wait (1976), Electromagnetic groundwave

propagation theory and experiment, Vol. XVII, Symposia

Mathematica, Instituto Nazionale di Alta Matematica, Bologna

(published by Academic Press).

-88-
APPENDIX Bl

USER'S GUIDE, LISTING AND SAMPLE OUTPUT

FOR PROGRAM WAGNER

Card 1: KIND, TD (IlO, FlO.O)

KIND = beginning type of distance at which F(x)

will be evaluated

1 is specified on next cards

Ois equidistant

TD = total distance in kilometers

Card 2A: X(I)

X(I) = (8FlO.5)

specific distances in kilometers at which F(x)

will be evaluated.

IF KIND = I use these cards to begin giving

specific distances until you are done or want

to change to equidistant points.

Terminate this set of distances with a o.

Card 2BI: NED

NED

(12 )

= number (limited to 50) of consecutive sections

with F(x) evaluated at equidistant points.

(This should agree with the number of pairs of

DEP and FINT).

Card 2B2: (DEP (I) , FI!'JT (I) , I = 1,NED) (8FIO.O)

DEP(I) = distance in kilometers at which this set of

equidistant points ends.

FINT(I)= interval of these equidistant points in

kilometers

If KIND= 0 use these cards to begin.

N.B. There may be a series of 2A and 2B cards to reach the

total distance given on card 1.

Card 3: HA, FREQ, POL, HAR, AKM, MF, IDATA, SF (5FlO.S,212,FlO.0)

HA = transmitter antenna height in kilometers

FREQ = frequency in MHz

POL = polarization; 1 is vertical, 2 is horizontal

HAR = receiver antenna height in kilometers

AKM = earth radius in kilometers

MF = 0 (no microfilm); MF 0 (microfilm)

IDATA = O(no measured data input); IDATA 0 (measured

data input and plot)

SF = scale factor for microfilm

Card 4 ID

ID

(8AIO)

path identification

-89-
Card 5: N, IXUNITS, IZUNITS, REFEL (3IIO,FIO.l)

N = number of points on terrain profile

IXUNITS = 0, distance input in kilometers

= 1, distance input in statute miles

IZUNITS = 0, height input in meters

= 1, height input in feet

REFEL = reference elvation in lZUNlTS(=height at d=O)

Card 6

to M: (X (I), Z (I), I = 1, N) ( 4 (F1 a . 2 , Fla. 0) )

X(l) = terrain distances in IXUNITS

Z(I) = terrain heights in IZUNITS

End with -1. ·in X field

Card M+l: NGC (lID)

NGC = number of sets of OX, SIGX, EPSX

(limited to 50)

Card M+2

to end: (OX(I), SIGX(I), EPSX(I), I = 1,NGC)

(4 (F7. 0,F7. 4,F6. 0))

OX(I) = maximum distance in kilometers for given

sigma and epsilon

SIGX(I) = sigma

EPSX(I) = epsilon

**Measured data input cards follow last of above cards;

distances (OD(J), see WAGPL) are in km;

format: d(km), OBU - (8X,6(F6.2,F6.0)

End with -1. in d m field. .

Output: DBU = 106.92-201og d km + 20 log2IF(X) I

-90-
PROGRAM WAGNERCINPUT,OUTPUT,TAPE60=INPUT OIH£NSION IPOl(Zl OI"ENSION ADAB(3),ADGH(3) COMMON 101 F(2000).R13(2000),R14(2000t,Rl~(2000J,R16(2000J.Rl1(200

10l,~18(2000),R19C20DO),R20(2000),R21(2000)

COMMON/1l HA,AKH

gg~~g~ ~~~ gEtt~k.WAVE COMMON 141 FREQIPOL COMMON 151 NG,AB(48),GHC48l CC~~ON 161 N,X(lD01),INOEX

COMMON. ISINI SUH.. P.,NITtSX.1501.). ,5.Z(~01).. ,AlF(501) COM~ON IINPUTI DUMHllu320),IO(8).REFEL

COMMON IGeXI NGC!DX(50),ETAX(SO),OElTAX(SO),SIGXfSOJ,EPSXC50) COMPLEX ETAXtOElTAX

OOUQlE PRECI~ION OA8.DGH

COMPl. EX FE.W.~.FIAlAMZtSUH,O.. ELTAR,ETAR COMPLEX KERNl,pO,Pl,P2,P3.Pl+.CTHP CO~PlEX FF,ETA,OElTA DATA (NG=5t DATA (AOAB=.9061198459,.5384693101,O.) DATA (AOGH=.2369268851,.4186286104,.5&888888888) CANG(Z)=ATAN2(AIMAG(Z),REALCZ)

IPOL(1)=8H VERTICSIPOL(Z)=8HHORIZONT C

C READ GAUSSIAN QUAOQATURE AeCISSAS AND WEIGHTS

C NR=(NG+l)/Z

00 1 L=l,NR OAB=AOABCl)

OGH=AOGH(L)

J=NG-L+l ABfL)=OA8

ABfJ)=-AB·(L)

GH(l)=OGH 1 GHfJ)=GHfl) C

C CAll SUBROUTINE TO SET UP OISTANCE AR~AY X "IN METERS

C START WITH X(Z), X(l)=O. HAS ALREADY e~EN SET.

e THE DISTANCES 00 NOT HAVE TO BE EQUALLY SPACED.

C SUBROUTINE orSTX SHOULD MAKE SURE N 2000

C

l+ X( 1) =0.

F(1)=(1 • .l0.) CALL OISTX

C

C HA~E SURE THERE ARE AT LEAST 4 DISTANCES

IF (N.Gf.4) GO TO Z

PRINT 18

CAll EXIT

C

2 SQ~TX2=SQRT(X(Z»

SQQTX3=SQRT(X(3»

SQRTX4=saRTCX(4»

01=SQRT(X(Zl.X(!).X(4».(X(2).(SQRTXl+-SORTX3)+X(3)·(SQRTX2-SQRTX4)

1+X(4)*CSQRTX3-SQRTX2»)

~1=X(3)·X(4)·(SQRTX4-SQRTX3)/Ol

RZ=~(2)·X(4)·(SaRTX2-SaRTX4)/a1

R3=X(Z)·X(3)·(SQRTX3-SQRTXZ)/Ol

~4=(X(Z).(SQRTX4••3·SQRTX3 •• 3)+X(3).(SQRTX2•• 3-SQRTX4·-])+X(4.·1SQ 1RTX3··!-SQRTX2··3)./Ol

RS~~ORT(X(31·X(4»)·(X(3)·X(4))/01

R6=SCRT(X(2,·X(l+»4(X(4)-X(Z»/Dl

~7=saRT(X(Z)·X{3)t·(X(2t-X(3»/Dl

R8=(SQRTXZ-tSQRTX3··3-SQRTX4 ••3)+SQPTX3.(SQRTX4••]-SQRTXZ··3)+SQRT lX4·(SQ~TXZ··3·SQRTX3··31)/D1

R9 ::SQRT«X ( ~) • X(4 ) ) • ( SQRTX4- SQRTX3) 10 1 R10=SQ~T(X(2)·X(4t)·(SaRTX2-SQRTX4)/Ol

Rl1=SQPT(X(Z)·X(3»)·(SQ~TX3-SQRTX2)/Ol

-91-
3

8

C

C

C

C

C

R12= CSQRT XZ- I XIitt -x 13 t t +SQRT X3 - I X(2) -x IIt) H SQRTX it- IX(3 ) - X12t t ) /)1 00 3 M=S,N H1=M-1

1'12=1'1-2 OELTA1=XIMt-XIH1)

OELTA2=XCMt-XIHZ)

DZ=COELTA1-0ELTAZ)·OELTA1-0ELTA2

~13(~)=XIM1)-XIH2)-IXIHZt-XIH1»)/02

~14C~)::XCM)-XIHZ)·IXCM)-XCHZ»/OZ

R15IM)=XCHt-XIM1)·IXCM1)-XCM)'/02

Rl&CMt=IXCH1)44Z-XIM2)--Z)/02

R17IM)=IXIM2t 4 4Z-XIH)·4Z)/OZ

R181~)::IXIMt--2-XIHl)·-2)/D2

R1~CMt=CXCHZ)-XIH1)/02

RZOI~)=IXCH)-XIMZtt/OZ

RZ1IH)=IXIM1)-XIH)t/02

READ SOURCE HEIGHT, FRfQUENCY, AND POLARIZATION

COL OESCRIPTION

1-10 SOURCE HEIGHT, KH

11-20 FREQUENCY! MHZ 21-30 POLARIZATION, 1. = VERTICAL, 2. = HCRIZONTAL

READ 19, HA.FREQ,POL.HAR,AKM

IQT=O

HAR=HAR-l.E+3

HA=HA·1.E3 KPOL=POL

ALAH=2.997925E2/FREQ

WAVE=&.28318S307/ALAH

ALAHZ=CCO.70710&7812,0.707100781ZtISQRT IALAM»

TO=SECONOIDUH) C

C LOOP ON DISTANCE

C

51

52

C

C

C

£>

7

00 14 I=1,N IND~X=I

IF II .NE. U GO TO 51 CALL TERRAN2IXlIttH.HPlETA,OELTA.ETAR,DELTAR.CONO,EPS) PRINT 20, FREQ,IPoL(KPuL),AKH.~A,HAR

GO TO 152 CALL TERRANE IXII),H,HP,ETA,OELTA,ETAR,DELTAR,CONQ,EPS) COhrrNUE

IF II.fQ.U GO TO 1it

O=XClt+(H·-Z)/IZ.-XCI»

FII)=FEWH(H,XII»

IF II.LE.o) GO TO 13

J :: Z THROUGH it

SU~= 10 • , O. ) 00 9 J=Z,4 PO=P1=PZ=P3=IO.,0.)

K=J-1 XPZ=O.S-IXIJ)+XIK)t

XMZ=O.~·(XIJt-XIK»)

00 7 M=1,NG XO=XP2+ABIM)-XHZ

CTMP=KERNLIXOI-GHIM) P1=Pl+CTMP-SQRTIXO)

PZ=P2+CTHP-XD

P3=P3+CTMP-SQRTIXO)--3

I F I K. NE • 1 t GOT 0 0

XO=O.ZS-XIJ)-I1.+ABOO t--z PO=PO+~JRT(XO)·KERNLIXO)·GHIH)

GO TC 7 PO=oO+CTMP

CONT INUE

-92-
8

q

C

C

C

10

11

C

C

C

12

14

16

c

c

GO TO 4

-93-
18

19

20

2Z

1

2

COMPLEX FUNCTION KERNL(XO) COH~ON/ll HA,AKH CO~HON IZI O,HtHP COMMON 131 DEL ARt WAVE COMMON 141 FREQIPOL COMMON lSI NG,A~(48),GH(48)

COMMON 161 NX,XCZ001),I CO"PLEX FEWH,OELTA,OELTAR1ETA1ETAR CALL TERRANE (XO,HO,HPO,ETA,OtlTA,ETAR,OElTAR,CONO,EPS) XHS=XU)-XO

HO=H-HO

Rl=SCRT(XO··Z+HA··Z)

Rw=WAV"· (X O+c (HO·· Z) I ( Z.· X0) ) +XMS+ ( (HO" 2) I ( 2. ·XMS) )..0' KERNL=CMPLX(COS (RW),-SIN (RW».SQRT(X(I)/(R1.XM$)'.«HPO+DELTA-DE lLTAR)·F~WH(HO,XHS)-(HO/XMS»

RETURN

END

-94-
c

c

c

c

c

2

,.

6

7

8

10

12

14

16

18

20

100

101

10~

103

SUBROUTINE OISTX

SUBROUTINE TO FILL DISTANCE ARRAY. USE EITHE~ SPECIFIC

DISTANCES (KINO = 1) OR COMPUTE DISTANCES AT EQUIDISTANT POINTS (KINO = 01. A COMBINATION OF THE TWO KINOS CAN BE

USED. ALL VARIABLES ARE REAQ fN IN KILOMETERS AND THE DISTANCE ARRAY IS FILLED IN MEERS.

COMMON /6/ N,XIZ001),INOEX DIMENSION OEP(50)~FINT(50)

N=2 READ 100, KIND,TO TOH=TO·l.E+3

IF (EOF(60» 8,2

IF (K I NO ) .. , 12

00 6 L=N,2001,8

K=L+7

READ 101, (XtI), I=L,K) DO 6 J=1,8 N=L+J-l

IF (XfN) .LE. 0.) GO TO 10

XCN)=)«N)·1.E+3

CONTINLE

PRINT 102

CALL EXIT

IF (X ( N-l) .L T. TOM) GO TO 1 2

N=N-1

RETURN

REA1 103, NEO,(OEPCI),FINT(I), I=l,NEO)

~~P~~D~plf~~Y.E+3 FINTM=FINTCII·1.E+3

SV=.l·FINTM

00 14 J=N,2001 JS=J X(J)=FINTM+XfJ-l)

IF (X(J» .GE. (TOM-SV)) GO TO. 16

IF (X (J) .GE. (OEPM-SVI) GO TO 18

CONTINUE

GO TO 7

X(JS)=TOM

N=JS

RETURN

)«J<;)=CEPM

N=JS+l

CONTINUE

GO TO I.t FOQMAT (Il0,FtO.O) FCQMAT (8F10.';) FOQMAT (.ONUHBER OF DISTANCES EXCEEDS OIH~NSION·)

FOR~AT (I2/(8Fl0.0) END

-95-
COMPLEX FUNCTIONWERF(ZZZ) COMPLEX Z,ZZZ,ZV,~,Z2,C,W,S

DIMENSION C(i2), W(S,4) EQUIVALENCE (S,C(12» LOGICAL LZ2

DATA (C(1):(.O,-.5641895835» OATA « (W(I ,J) , I =1 ,5) , J= 1, 4) =(1. ,. 0) , X f3.678794411714423E-01.6.0 71~77058413q37E-01),

X (1.e31563888873418E-02,3.400262170660&62E-Ol), X (1.234098040866788E-04,2.011573170376004E-Ol), X (1.125351747192646E-07,1.4595358QQ001528E-Ol), X (4.275835761558070E-01,O.OOOOOOOOOOOijOOOE+OQ), X (3.047442052569126E-Ol,2.082189382028316E-Ol), X (1.402395813662779E-Ol,2.222134401798991E-01),

X (6.531777728904697E-02,l.739183154163490E-Ol),

X (3.628145648998864E-02.1.358389510006551E-Ol), X (Z.553QS6763105058E-Ol.0.000000000000000E+OO).

X CZ.184926152746907E-Ol,9.299780939260186E-OZl,

X 11.479527595120158E-Gl,1.311797170842178E-Ol), X Iq.271076642644332E-02,1.283169622282615E-Ol), X (5.Q6869Z961044SQOE-02,1.1321005&1244882E-Ol), X (1.790011511813930E-01,O.OOOOOOOODOOOOOOE+QO), X (1.6~261136392q861E-OltS.019713513~24966E-02),

X (1.3075746q6698S22E-Ol,8.111265047745~7ZE-02),

X rs, n40250558304439E-02,q.1236326004Z1258~-OZl,

X f6.919096164964750E-02,8.934000024036461E-OZ»

XX=PEALCZZZ)

YY=AIMAG(ZZZ)

X=AC3S (X)

Y=ABS fYY) Z=CMPLX(X,Y)

lZ2=.FALSE.

IF (X.GE.4.5.0R.Y.GE.3.5) GO TO 6

I=X".5

J=Y+.S

V=CMPLXCFLOAT(1),FLOAT(J»

ZV=Z-V

C(2)=WCI+l,J+l)

AI=O.

00 1 1=3,12 AI=AI-.5

C(I)=(~·C(I-l)+C(I-2»/AI

1 COt\TINUE

J=12

00 2 1=2,11

J= J-l

2 S=S·ZV+C(J) 3 IF (YY.GE.O.) GO TO 4

IFf.NeT.LZZ) Z2=Z·Z

S=2."'CEXP(-ZZ)-S

IF (XX.GT.O.) S=CONJGIS) GO TO 5

I.t IF (XX.LT.D.) S=CONJG(S) 5 WE~F=S

~ETURN

6 LZ2=.TRUE.

Z2=Z·Z

S=Z.((O.,O.1.t613135279J/(Z2-0.1901635092)+(O.,O.099Q921 6 16 8 . ,

1(Z2-1.781.t4927485)+(O.,O.002883S938748)/(72-5.5253437437q»)

GO TC 3

END

-96-
ADJUSTED PATH PROFILE FOLLOWS

o IN METERS

1 0.00000

Z 885.11500

3 1617.34650

it 1E73.6720Q

5 2092.09000

6 5045.15~50

7 52ltE.31800

8 5423.34100

q & 533. 75 eo Q

10 7Zg0.12QOO

11 7721.~2140

12 r917.7S600

13 8046.50000

14 8199.38350

15 8690.22000

16 8835.05700

17 9100.Sg150

18 919~.75880

19 9659.01860

20 10219.05S00

21 10363.89200

22 10870.82150

23 11031.7~150

24 111;2.44~OO

25 11400.28120

26 11852.4Q450

27 123~1.61000

28 1278;.888;0

29 12954.86500

30 13209.13440

31 13389.37600

32 134Q3.98050

33 13~82.4920a

34 13679.05000

35 13791.70100

36 13896.30550

37 1~214.~ql00

38 1~523.q3250

39 14g18.21100

40 1511Q.37350

41 152~8.11750

~? 1~~44.67;SO

43 1~52q.74S00

44 16374.62750

45 17332.16100

46 17380.44000

47 17460.90~OO

46 17670.11400

49 17959.78800

50 18185.09000

51 1~311.60000

-97-

HT IN METERS

a.ooooo

-8.53440

-13.71600

-11.58240

-11.58240

12.80160

12.80160

15.84960

37.18560

53.34000

75.59040

128.62560

130.45440

125.57760

92.04960

95.0g760

103.63200

100.58400

128.62560

135.33120

13ft.72160

95.09760

63.39840

98.1t+560

143.86560

147.82800

140.81760

98.14560

94.48800

80.46·720

101.19360

102.71760

91.7'+480

99.97«'40

105.15600

96.62160

140.81760

105.15600

165.20160

165.20160

149.96160

149.96160

128.62560

100.88880

100.~8880

98.14560

98.1'+560

107.28Q60

116.43360

116.43360

92.04960
BOULDER TO S.E. (OAVIDSON H~SA )

NUMBER OF PROFILE DATA POINTS IS 51

REFERE NeE ELEVATION IS 1608.73 METERS

PATH PROFILE AS PUT IN FelLOWS

0.00000 5278.0 .55000 5250.0 1.00500 5233.0 1.04000 5240.0

1.30000 52&+0.0 3.131500 5320.0 3.26000 5320.0 3.37000 5330.0

4.06000 5400.0 4.53000 5453.0 4.79800 5526.0 4.92000 5700.0

5.00000 5706.0 5.09500 5690.0 5.40000 55 eo. 0 5.49000 5590.0

5.65500 5618.0 5.71600 5608.0 6.00200 5700.0 6.35000 5722.0

6.44000 C;720.0 6.75500 5590.0 6.85500 5486. a 6.93000 5600.0

7.06400 5150.0 7.36500 5763.0 7.70000 5740.0 7.94500 ~600.0

8.05000 5588.0 8.20800 5542.0 8.32000 5610.0 8.38500 5615. a

8.4ltOOO ;579.0 8.50000 5606.0 8.57000 5623.0 8.63500 55CJ~. 0

8.87000 5740.0 9.02500 5623.0 9.27000 5620.0 9.39500 5820.0

9.47500 15770.0 9.53500 5770.0 9.65000 5700. 0 10.17500 5609.0

10.77000 5609.0 10.80000 5600.0 10.85000 5600.0 10.98000 5630.0

11.16000 5&60.0 11.30000 5660.0 12.00000 5580.0

-98-
c

c

c

c

c

c

c

c

c

C

lS02

1503

1504

1505

1506

1510

1511

1512

1513

1'51~

1;15

1516

105

120

130

110

SUB~OUTINE INCN) CO~MON IINPUT/X(SOOO), Z(~OOO), A(120f t 8(120), AA(40), Ae(40)~ 10 1(8),REFEl

CO~MCN /GCXI NGC,OXfSO),ETAX(50),OEL1AX(gO),SlGXC50),tPSX(50)

gg~~r~'4~T:~;gEr~kx

INPUT

10 = ICENTIFICATION

N = NUMBER OF DATA POINTS

IXUNITS =0, DISTANCES INPUT IN KILOMETERS

I.. XUNI... T... S =1, DIS.. T. A... NC..£S. I. N.PUT IN ".... 1. LeS IZUNITS = O. HEIGHTS INPUT IN METERS I~UNITS =1, HEIGHTS INPUT IN FEET

REFEl = REFERENCE ELEVATION IN METERS

FQRMAT (8AI0) FORMAT (2X,8Al0) FORHAT C4CFI0.5,FI0.1» FO~MAT (4fFl0.2,F10.0) FORMAT fl0X,I10,2F15.5) FO~MAT (3II0,F10.1) FOQMAT (2X ••NUHBEQ OF PROFILE DATA POINTS IS·II01

C2X,·REFERENCEELEVATION IS·FI0.2.·METERS.'

ClXt·PATH PROFILE AS PUT IN FOLLOWS·/) FO~~AT (II. THE NUMBER OF SCALED DATA POINTS HAS EXCEEDED ~OOO OR

1THE NUMBER OF GROUND CONSTANT PAIRS HAS EXCEEDED 50·) FORMAT (·OAOJUSTEO PATH PROFIl£ FOLLOHS./23X,. 0 IN METERS·,3X,

l·HT IN METERS·) FO~HAT(1H1)

FORMAT (·0·12 •• DISTANCE AND GQOUNO CONSTANT PAIRS FOLLOW·, 111X,·O IN KH·,3X.·SIGMA·,2X,·EPSILON·/

C(10X,F8.3,F8.4,F9.0»

FO~MAT (4(F7.0,F7.4,F&.O» FTOM = .3048

EP = - 5

ZO = I.E-3

READ ·1'302, 10 PRINT 11514

PRINT 1503, 10

READ 1;10, N,IXUNITS,IZUNITS~REFEl

IF (IZUNITS.EQ. 1) REFEL=REFEL4FTOH

IF fN .GT. 5000) GO TO 110 P~INT 1511, N,REFEL READ 1505, (X(I),Z(I)i I~l,N)

PRINT 1504, (xtI)f Z( ), I ':: 1. N) IF fN .IT. 1t GO 0 120

PRINT 1513

XCONST=1000.

IF CIXUNITS • Ea. 1) XCONST=160g.3 ZCO~ST=l.

IF (IZUNITS .EO. 1) ZCONST=FTOM

00 105 I :: 1, N

Z(I)=Z(IJ4ZCONST-REFEL X(I)=X(I)·XCONST

PRINT 1~06. I, X(!), Z(I)

CONTINUE

CO~TINUE

i~A~Natl~GT~G~O) GO TO 110

~EAO 1~16, (OXCI)tSIGXCI),EPSXC!Jl I=l.NGCl

P RIN T . 1515, NGC. ( ox(I) ,S I GX( I) • Ep~ X( I), I 1 t NGC) 00 130 I=1,NGC ETAXCI)=CMPlXIEPSX( ),-17Q 5.·SIGX(Il/FREQ) OElTAX(I)=CSQRTCETA (1)-1. IF (POL .EQ. 1.) DE TAXCI' nELTAX(!)/ETAXCI) OX(I)=CX(I)·1000.

RETURN

CONT INUE

PR!NT 1'512

tNO

-99-
SUBROUTINE TERRANE (X,H,HP,ETA,OElTA,ETAR,OELTAR,CONO,EPS) C SUBROUTINE FOR WAGNER. OEFINEi TERRAIN.

C SMOOTH SPHERE

COMMON/INPUTI TO(5000) ,THT(5000) " COMMON IGCXI NGC,DX(50),ETAX(SO),OELTAX(~O),SIGX(,O),EPSX(SO)

COMMON ITEST21 SXHIN(100),SXMAX(100) COMMON ITERMAI ICOUNT,XO(100),AN(100),ALPHA(100) COHMON/i/ HA,AKM COMPLEX ETAX,DELTAX,ETAR,DELTAR.ETA.DElTA

C

C COMPUTE HEIGHT,SLOPE,CONOUCTIVITY AND DIELECTRIC CONSTANT AT X

7 CONTINUE

IF (X .GT. TOCNt) X=TO(N) A=1000.·AKM

_HP=-X/A

H=.t;·X"HP-HA

00 6 I=2 9N

IF IX .GT. TOIl» GO TO 0

H=H+THT(!-l)+(IX-TO(I-l»)/CTO(I)-TO(I-l»)·(THTCI)-THT(1-1»

HP=HP+(THT(I)-THT(I-1»/(TOfI)-TOfI-l»

GO TO q

6 CONTINtJE

9 CONTINlE

00 2 1=11.50

IF (X .Lf:.. (OX(I)+.0001» GO TO ft.

Z CONTINUE

4 ETA=ETAXCI)

OEL TA=OEL TAXI!l

CONO=SIGX(!)

EPS=EPSX(I)

RETURN

ENT~Y TERRAN2

CAll IN(N) ETAR=ETAX(1)

OfLTAR=OELTAX(1)

GO TO 7 ENf')

-100-
DISTANCE AND GROUND CONSTANT PAIRS FOLLOW

o IN KM SIGMA EPSILON

19.320 .01~0 15.

FREQUENCY 1.49

TRANSMITTER ANTENNA HEIGHT

VERTICAL POLARIZATION EARTH RADIUS = 45.800 METERS RECEIVER ANTENNA HEIGHT

8500. KH

6.000 HET~RS

x

(M)

Z

(M)

HT

FT

CONDUCTIVITY

(MHO/H) QIELECT~IC

CONSTANT HAG

F(X)

ARG

TIMING

(SEC)

FIELD STRENGTH ~TL

HI (OBU)

I

.......

o

.......

I

100.00

200.00

300.00

.. 00.00

500.00

600.00

700.00

800.00

900.00

1000.00

1100.00

1200.00

1300.00

1.. 00.00

1500.00

1600.00

1700.00

1800.00

1900.00

~ooo.oo

2100.00

2200.00

2300.00

~400.00

2500.00

-"6.e

-47.7

-48.7

-51.6

-53.6

-55.2

-55.CJ

-57.4

-58.1

-58.e

-59.5'

-57.6

-56.8

-55.2

-54.4

5274.e

5271.~

5268.4

5265.3

-;262.1

5259.0

5247.3

52"2.6

52"0.3

5238. 0

5235.7

5233.3

5240.2

5245.6

524 e. 3

52Ci1. 0

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

15.0000

15. 0000

15.0000

15.0000

15. 0000

15.0000

15. 00 a0

15.0000

15. 0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

1,5. 0000

15.0000

15.0000

15 •. 0000

15.0000

15.0000

15. 00 00

15.0000

15.0000

.9.. 279026E+00 -.15563449£+00

.92377247E+00 -.2.... 50719£+00

.91613104E+00 -.28027497E+00

.90767002£+00 -.35311718E+00

.90227283£+00 -.38219743£+00

.89800930£+00 -.40852044E+00

.89434598£+00 -.43288575E+00

.a9012764E+00 -."5677281E+00

.88584348E+00 -.479765~3E+00

.86157101E+00 -.50189017~+00

.87314729E+00 -.54379204E+00

.86900763E+00 -.56370025E+00

.8e64~129E+00 -.5588072&E+00

.87413320£+00 -.58556513E+00

.86949036E+00 -.60438860E+00

.86545442£+00 -.62207703E+00

.86304316E+00 -.63736481E+00

.86437172E+00 -.64759220E+00

.86285.. 70f+00 -.66085001~+00

.86067900E+OO -.67458127E+00

.85816499E+00 -.6R841967E+00

.153

.156

.169

.174

.215

.261

.315

.372

.427

.501

.574

.649

.73"

.825

.920

1.020

1.128

1.245

1.363

1.488

1.61&

1.748

2.044

.1 132.48

• 1 126.33

.2 122.71

.2 120.13

.3 118.12

.4 116.51

.4 115.12

.5 113.91

.6 112.84

.6 111.89

.7 111.02

.7 110.22

.8 109.49

.9 108.60

.9 108.16

1.0 107.56

1.1 107.21

1.1 106.59

1.2 106.07

1.2 105.59

1.3 105.14

1.4 104.75

1.4 104.35

1.6 103.57

10.35

16.50

20.12

22.70

24.71

26.32

27.72

28.93

29.'99

30.94

31.81

32.61

33.35

34.03

34.67

35.27

35.63

36.25

36.76

37.25

37.70

38.03

38.49

38.88

39.26
2600.00

2100.00

2800.00

2900.00

3000.00

3100.00

3200.00

3300.00

3.. 00.00

3500.00

3600.00

3100.00

-53.6

-52.0

-51.2

-50...

-"'.3

·"5.1

- ..... 9

5253.7

5261.8

5272.7

5278.1

5280.8

5283. S

.015000

.015000

.015000

.015000

.015000

.015000

.01S000

.015000

.015000

.015000

.015000

.01S000

15. 0000

15. 0000

15.0000

15.0000

15.0000

15.0000

lS.0000

15.0000

15. 0000

15.0000

15.0000

15. 0000

.8554.. 078E+00 -.70222787E+00

.85l57383E+00 -.71,)9"03~E+00

.84656175E+00 -.74295S11E+00

.8.. 3..6287E+00 -.75622773E+00

.8.. 032247E+00 -.76933~11E+00

.83715111E+00 -.78227523E+00

.63395700£+00 -.79504817£+00

.8307..658E+00 -.e07&5'53~E+00

.82752502£+00 -.82009906E+00

.82429651£+00 -.83238222£+00

.82106441E+00 -.8445060~E+00

2.195

2.350

2.514

2.681

2.850

3.022

3.206

3.404

3.603

4.034

4.252

1.6 103.21

1.1 102.85

1.7 102.50

1.8 102.17

1.9 101.84

1.9 101.52

2.0 101.21

2.1 100.91

2.1 100.62

2.2 100.34

2.2 100.06

2.3 9q.78

39.63

40.33

40.67

41.31

41.62

41.92

42.21

42.50

42.78

43.05

I

.......

o

t\.)

I

3800.00

3900.00

"000.00

"100.00

"ZOO.OO

"300.00

.... 00.00

..500.00

..600.00

.. ,00.00

"&00.00

.. 900.00

5000.00

5100. 0'0

5200.00

5300.00

5"00.00

- ..... 1

- .. 1.&

-39.5

-38.7

-37.9

-36...

-35.6

-34.8

-34.6

-33.1

-32.1

5305.2

')307. s

s 310. E

5316.0

5323.0

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.0 IS 000

.015000

.015000

.015000

15. 0000

15. 0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15. 0000

15.0000

15.0000

15.0000

1'5.0000

IS.0000

15.0000

15.0000

15.0000

.8118317.. £+00 -.856.. 8016E+00

.81460066£+00 -.86830204E+00

.61137320E+00 -.81Q97139E+00

.60815101£+00 -.89150Q86E+00

.80493548£+00 -.90290308£+00

.80172719£+00 -.91416062E+00

.79852895E+OO -.92528595£+00

.19533980E+00 -.93628247E+OO

.19216107E+00 -.94115348E+00

.78899338£+00 -.95190218E+00

.785831l5E+OO -.9685316&E+OO

.11956141~+00 -.989~4485E+00

.11129129E+00 -.100&1421E+Ol

.166501Q8E+DD -.10Z0Z821E+Ol

• 712 0 13 11 E+00 -. 1 0191 &61 £ +0 1

.17130113E+00 -.10244&3&E+Ol

4.483

4.122

4.964

5.212

5.410

5.718

5.911

6.237

6.501

6.791

1.074

1.667

7.978

8.301

8.615

8.939

2.4

2.1

2.1

2.8

3.0

3.0

3.1

3.2

3.2

3.3

3.4

99.26

99.00

98.16

q8.51

98.21

98.04

97. e 1

97.36

q1.14

96.93

96.72

96.45

96.13

95.96

43.31

43. ~7

44.08

44.32

44.80

4S.03

45.2S

46.11

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6600.00

6100.00

6800.00

6900.00

1000.00

1100.00

7200.00

7300.00

1"00.00

7500.00

1600.00

1100.00

1800.00

1900.00

8000.00

8100.00

6200.00

3300.00

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.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

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.015000

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.77210049£+00 -.10283088£+01

.11160151E+00 -.10336.. 92E+Ol

.77040006E+00 -.10"02 .. Z2E+Ol

.16686.. 58E+00 -.10470401E+Ol

.7671025..E+00 -.105.. 0962E+Ol

.16511606£+00 -.10613300E+Ol

.76312.. 91E+00 -.10666818E+Ol

.76097632E+00 -.10761168£+01

.7;87499.. E+00 -.10836086E+Ol

.756.. 60 ..3E+00 -.10911377£+01

.1~"11g11E+OO -.10986893E+Ol

.7528 ..12 .. E+00 '-.110..6127E+Ol

.75118736£+00 -.11110230E+Ol

.14915473E+00 -.11178563E+Ol

.74700006E~OO -.112.. 8154E+Ol

.7.... 76560E+00 -.11318433E+Ol

.7.. 247308E+00 -.11389108E+Ol

.7401359Z£+00 -.11460000E+Ol

.7.. 3 .. 2751E+00 -.11450 .. 62E+Ol

~~5671995E+OO -.11293030E+01

• 7616 .... 0..E+00 -.11249129E+01

.76449450E+00 -.11233491E+Ol

.76623259E+00 -.11232917E+Ol

.91615554E+00 -.g7624953E+00

.97680880E+00 -.93564700E+00

.82579187E+00 -.10853Z06£+01

.7693"993£+00 -.11C;18593E+Ol

.73671"88~+OO -.12008081E+01

.68999117E+OO -.12BZ0878~+01

.66"156~3E+00 -.13360839E+01

9.278

9.607

10.283

10.631

10.99"

11.353

11.711

12.096

12.1+95

12.879

13.275

13.665

14.071

14."78

11+.877

15.30B

15.1"0

16.170

16.611

17.048

17."99

17.981

18."68

19.387

19.882

ZO.371

20.81+7

21.352

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3.7

3.7

3.8

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4.0

4.1

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".6

".7

".7

4.8

4.8

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5.0

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5.2

5.2

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95.11+

94.81

9".64

94.31

94.15

94.00

93.85

93.70

93.55

93.40

93.25

93.10

93.02

93.00

9Z.91

92.82

94.26

93.14

g2.41

91.26

gO.82

47.a3

47.69

47.86

48.03

"8.19

48.36

48.52

48.68

..9.13

49.28

.. 9.58

49.73

49.84

C;0.01

48.13

"9.70

50.42

«;0.90

52.01
8500.00

8600.00

~700.00

8800.00

8900.00

<3000.00

<3100.00

9200.00

<3300.00

9400.00

9500.00

9&00.00

9700.00

42.0

4&.7

52.9

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&1.8

73.8

77.8

5622.6

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55.,0.6

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5628.2

564 e. 2

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.015000

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.015000

.015000

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15.0000

15.0000

15.0000

15.0000

1C;.OOOO

15.0000

15.0000

15. 0000

15. 0000

15.0000

15.0000

15.0000

.6~435314E+OO -.13823602E+01

.&2810068E+OO -.14239253£+01

.62819893E+00 -.14362S45E+01

.65;30810£+00 -.13872.. 33E+01

.66158202E+00 -.13637021~+01

.61"30175£+00 -.13S02801~+01

.67747167E+00 -.13430412£+01

.64630760£+00 -.13978S11E+Ol

.&9489619£+00 -.131&5227E+01

.10122613£+00 -.13048481E+01

.70551642E+00 -.12966229£+01

.68824315£+00 -.13201305£+01

21.836

22.3~C;

22.887

Z3.440

23.967

25.069

ZC;.628

26.172

26.736

27.305

27.872

2B.~57

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5.3

5.5

5.7

5.7

5.8

5.9

6.0

6.0

90.46

90.13

90.03

90.30

90.36

90.35

90. 30

89.79

90.20

90.24

90.22

90.19

52.7'J

52.80

52.47

52.48

52.5lf

53.04

52.60

52.61

52.65

52.95

I

o

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9800.00

9<300.00

10000.00

10100.00

10200.00

10300.00

10400.00

10500.00

10&00.00

10700.00

10800.00

10900.00

11000.00

11100.00

11200.00

11300.00

11400.00

81.0

82.1

83.2

71.8

&3.9

48.0

16.7

30.0

53.7

72.1

5705.5

5713.3

5717.3

5721.2

5120.e

5710.7

5633.7

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5571.1

r;C;D6.r;

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562 '3.7

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.015000

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.

.015000

.015000

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.015000

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.015000

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lS.0000

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15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15. 0000

15.0000

15.0000

.67362354£+00 -.13439386£+01

.&6588276E+00 -.13578996£+01

.65994386£+00 -.1369.... 05E+01

.6S493545£+OO -.13197468£+01

.650.. 9383E+00 -.13893047£+01

.6375&912E+00 -.14141394E+01

.60661946£+00 -.14160945E+Ol

.57705755E+00 -.15485786E+Ol

.55942110E+00 -.16011956E+01

.S4560230~+00 -.16469400E+01

".53399311£+00 -.16884998E+Ol

.49836122E+00 -.17945700E+Ol

.45675478E+00 -.19568510£+01

.&0721581E+00 -.16383810£+01

.61209473£+00 -.15243834E+Ol

.69701701E+OO -.1~56~313£+01

.12011172£+00 -.1~035918E+Ol

29.01+1

29.637

30.26&

30.890

31.520

32.11+8

32.786

33.396

31+.017

35.283

35.925

36.582

37.21+1

31.909

39.303

6.1

&.2

6.2

f>.3

6.3

6.5

6.5

6.1

6.8

6.8

7.0

7.0

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89.61 53.23

89.'+2 53.42

89.25 53.58

89.10 53.13

88.95 53.88

88.70 5~.1'+

88.18 51+.65

81.66 55.17

87.31 55.52

81.01 51;.82

86.1~ 56.0Q

86.06 56.77

85.23 57.61

81.62- 55.21

88.~3 C;c..41

8"8.66 5... 17

88.88 53.95
IIt&>OO.OO

I1t600.00

1.. 100.00

1 ..800.00

I1t900.00

1&>000.00

1&>100.00

15200.00

15300.00

15.. 00.00

15500.00

15600.00

15700.00

50.4

88.&>

103.6

106.2

106.0

96.3

83.8

12.1

66.2

62.1

5&60.<:

5710.~

5188.6

57.. Q.0

5711.2

5692."

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.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

.....316065£+00 -.20073215E+01

.53285673E+00 -.18031&>75E+Ol

.58170077E+00 -.17098563E+Ol

.60331610E+00 -.165~323~~+01

.55517741£+00 -.17159675£+01

.53980183E+00 -.17380105E+Ol

• 47 7.. 1 0 08 E+0 0 -. 18 8261 87E+ 01

...g46146.. E+00 -.1~56634o£+01

.44601608£+00 -.19672979E+Ol

.43165893E+00 -.20321646£+01

.....188008E+00 -.20150633E+Ol

."'550369E+00 -.20100308E+Ol

65.116

66.059

67.020

67.97&

68.955

69.999

71.060

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73.139

7... 186

75.21&

76.268

9.0 82.57

9.1 84.11

9.2 85.07

9.3 65.23

9.3 8".23

9.4 83.93

9.4 62.80

9.5 83.05

9.6 82.10

9.6 81.76

9.7 81.90

9.8 81.92

60.27

58.73

58.32

57.77

57.60

58.61

60.03

59.78

60.74

61.08

60.93

60.91

9.8 81.83

I

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15800.00

1&>900.00

16000.00

16100.00

16200.00

16300.00

16"00.00

16500.00

16600.00

16700.00

16800.00

16900.00

11000.00

11100.00

11200.00

11300.00

17ItOO.OO

.. 8.9

..5.4

39.3

39.1

38.CJ

38.7

38.5

38.3

38.1

37.7

5670.8

5660.1

56"9.3

5638.5

5627.7

5617.0

5608.<:

5608.~

5608. <:

560 e. e;

560e.<;

&>608.c;

560e.c:

5599.q

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

.015000

1S.0000

15.0000

15. 0000

15.0000

15.0000

15.0000

15.0000

15. aD00

15. DODO

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

• 44348Q7.. E+OO -.20172939E+Ol

.4407.. 4 .... £+00 -.20270714E+Ol

.4377..913E+00 -.20379752E+Ol

.43468 ....1£+00 -.2049..Z34E+Ol

.43162843E+00 -.20611289E+Ol

.42861101£+00 -.20729362E+Ol

.43069675£+00 -.207013E7£+01

.43646949£+00 -.20546269E+Ol

.4381.. 361£+00 -.2049239&E+Ol

.43869085£+00 -.20465681E+ol

.43665298E+00 -.20"54947£+01

.43825398E+00 -.20454603E+ol

.43761115E+00 -.20461632E+Ol

."3679435£+00 -.2047"182£+01

."3584872E+00 -.20491015£+01

• 43 48 05 1 0E+00 - • 20 r;11 2 71E+01

.42893334£+00 -.2071109ZE+01

77.327

78.348

79.345

80.350

81.361

dZ.403

83.428

84.441

85."50

86.495

87.519

86.59Z

69.&76

90.812

91.960

93.080

... 183

9.9

10.0

10.1

10.1

10.2

10.3

10.3

10.4

10.4

10.5

10.6

10.6

10.7

10. 7

10.8

61.72

81.60

81.49

81.37

81.26

81.25

81.31

81. 29

81.25

81.20

81.14

'81.07

81.01

80.87

6 0.70

61.01

61.12

61.23

61.35

61.46

61.57

61.59

61.52

61.54

61.58

61.64

61.70

61.76

61.97

62.14
I

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11S00.00

11600.00

11700.00

11800.00

l1CJOO.00

12000.00

12100.00

12200.00

12300.00

12400.00

1~00.00

12600.00

12100.00

12800.00

12900.00

13000.00

13100.00

13200.00

13300.00

13400.00

1350 0.00

13600.00

13700.00

13800.00

13900.00

1"000.00

14100.00

1"200.00

1"300.00

14400.00

91.2

91.9

92.6

91.&

90.2

88.8

87.3

1... 1

63.1

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30.6

34.7

..... 1

"7.S

39.9

51.4

64.9

57152.8

5755.7

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5634.7

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.015000

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15.0000

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1'5.0000

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15. 0000

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15.0000

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113.0000

15.0000

15.0000

113.0000

113.0000

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15.0000

15.0000

15.0000

15.0000

15.0000

15.0000

15. 0000

.63409268£+00 -.15059253~+01

.61S07716£+00 -.15249655E+Ol

.6041c)'586E+OO -.1'5366078E+01

.'5c)662999£+00 -.15457102£+01

.58192368E+00 -.15703709E+01

.57142468£+00 -.15c)12147E+01

.56401120~+00 -.16075 .. 61E+01

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.;5238785£+00 -.16356615E+01

.53641632£+00 -.16116802£+01

.4C)661133£+00 -.17812016E+Ol

.41715123£+00 -.18519S26E+Ol

.46260250£+00 -.19126164E+01

.46S22600£+00 -.19304934£+01

.47987619E+00 -.1896'5CJ17E+01

• 4127 1 444 £+00 -. 1915 26 S6E+ 01

."65CJ8385E+00 -.19395135£+01

.46128831£+00 -.lCJ599~96E+Ol

• 52S9S444E+OO -.16096914£+01

.54324818E+00 -.17671388E+Ol

.131363890(+00 -.18151229E+Ol

.5050S731E+00 -.164SQ62iE+Ol

.52886281£+00 -.17855831£+01

.51897365E+00 -.17961924E+Ol

.S0232221£+00 -.16 ..363 .. 3E+01

.;7626560E+00 -.16862.... 6E+Ol

.5902J836E+OO -.16;43930£+01

.5473181QE+OC -.17281416E+Ol

.47"91566~+00 -:1C)006080E+Ol

39.988

40.697

"1.409

42.116

42.851

43.592

44.336

45.064

45.782

46.551

"7.311

"8.012

48.636

"9.629

50.430

51.199

51.964

52.767

53.552

55.184

S6.018

56.854

57.7Z7

58.621

59.531

60."52

61.376

62.315

63.229

7.1

7.2

7.3

7.3

7.7

7.6

7. e

8.0

8.0

8.1

6.2

8.3

8.3

8.4

8.5

8.6

6.7

8.8

6.8

87. f,9

87. 35

87.12

66.42

66.23

86.06

85. CH

85.58

64.84

84.43

84.09

64.27

e... 07

83.88

e3.73

84.80

65.02

64.47

8... 26

64.37

8".02

8".83

85.09

65.24

8,..52

83.23

55.14

55.71

156.19

156.4?

56.77

'57.25

~8.41

58.74

58.76

56.56

58.76

158.95

59.10

58.03

58.37

58.S8

58.Z4

58.00

57.60

58.31

59.61
17500.00 36.0 560C;.5 .0113000 15.0000 .43981+ 176E+00 -.20416220E+Ol 95.308 10.9 80.P7 61.q7

17600.00 .. 0.2 561~.c; .015000 15.0000 .41+958361£+00 -.2011+01+24E+01 96.1+53 10.9 81.01 61.83

17700.00 ..... 0 5633.0 .015000 15.0000 • ..52071.... £+00 -.20032183£+01 97.565 11.0 81.01 61.83

11800.00 .. ,.0 56.. 3... .015000 15. 0000 • 452 15.. 30 E+00 -.19984660E+Ol 98.719 11.1 80.96 61.8~

1790 O. 00 ..9.9 5653.7 .015000 15.0000 • "5262595E+00 -.19928185E+01 99.916 11.1 80.92 61.91

18000.00 51.6 5659.<; .015000 15.0000 .4"50623"£+00 -.20015702E+Ol 101.068 11.2 80.12 62.11

16100.00 51." 56«;9. c: .015000 15.0000 .,.3827815E+00 -.20227858E+Ol 102.210 11.2 80.154 62.29

18200.00 50.8 5658. 9 .015000 15.0000 .43085762£+00 -.20 .. 05858E+Ol 103.357 11.3 80.35 62.4g

18300.00 .. 8 ... 5651. .015000 15.0000 .42229378E+00 -.20649614E+Ol 104.527 11." 80.12 62.71

I

I--' 18 .. 00.00 1+6.1 56..... 7 .015000 15.0000 ."1691939E+00 -.2081989I+E+Ol 105.678 11." 79.91 62.87

0

18500.00 43.7 5637.6 .015000 15.0000 • ..1257..22£+00 -.209660 .. 3E+Ol 106.811+ 11.5 79.83 63.01

I

18600.00 Itt.3 563 O. r; .015000 15.0000 .40881506E+00 -. 210~8"32E+01 107.958 11.6 79.70 63.13

18700.00 38.9 5623." .015000 15.0000 • .. 05 ....527E+00 -.212215 .. 9E+Ol 109.136 11.6 79.58 63.25

18800.00 36.5 5616.3 .01S000 15. 0000 • ..023 5635E+ 00 -.21337865E+01 110.318 11.7 79.47 63.36

18900.00 3,..1 5609.2 .015000 15. 0000 .3991+8110£+00 -.211+.. 8901E+01 111.542 11. 7 79.36 63.47

19000.00 31.8 5602.1 .015000 15.0000 .39677.. 68E+00 -.21555699E+Ol 112.813 11.8 79.26 63.58

19100.00 29." 5595.0 .015000 15.0000 .39420555E+00 -.21658962E+Ol 1'11+.051 11.9 79.16 63.68

19200.00 27.0 5581.9 .015000 15.0000 • 39 175066 E+00 -.21759221+£+01 115.251 11.9 79.06 63.78

19300.00 2,..6 5'5~0.8 .015000 15.0000 .38939259E+00 -.21856888E+01 116.451+ 12. 0 78.96 63.88

19311.60 21t.3 5579.C3 .015000 15.0000 .38912471E+00 -.21868064£+01 117.101 12.0 78.qS 63~8q
APPENDIX B2

INPUT, LISTING AND SAMPLE OUTPUT FOR PROGRAM INTEQ 7/24/78

Card 1:

Card 2:

LBL (8AlO)

LBL = path label

NPF, IXU, IZU (3110)

NPF = number of points on terrain profile

IXU = 0, distance input in kilometers

1, distance input in miles

IZU = 0, height input in meters

1, height input in feet

-:

Cards 3 to M: (PFX(J), PFZ(J), j=l,NPF) (4(FIO.2,FIO.0» limited

to 500 points

PFX(J) = terrain distances in IXU

PFZ(J) = terrain heights in IZU

Card M+l: HTA, HTB, FMHZ, ENO, IPOL (4FIO.0,I3)

HTA = transmitter antenna height in meters

HTB = receiver antenna height in meters

FMHZ = frequency in megahertz

ENO = N

IPOL= po~arization; 1 vertical; 0 horizontal

Card M+2: NGC (110)

NGC = number of sets of DX, SIG, EP

Cards M+3 to N: (DX(J), SIG(J), EP(J), J=1,NGC) (4(F7.0,F7.4,F6.0»

limited to 50 sets

DX(J) = maximum distance in kilometers for given sigma

and epsilon

SIG(J) = sigma

EP(J) = epsilon

-108-
1

z

5

PROG~AM INTEQ(INPUT,OUTPUT) COHliON/FIELDO/XI,HTA,O,HTB,F,FIELO,XINTZ,XINTP,NlIHIT COMPLEX FIELD .

COMMON IPROFILEI GE,NPF,PFX(500),PFZC50Q) COHMON IHEADI LeL(8)

OATA(NLIHIT=200)

DATAeXZQ=0.S),(XXZ=10.),(NPO=4)

AD8(Z)=-4.34Z944819·AlOGCREALCZ)··Z+AIMAG(Z)··Z)

XI=100.

CONT INUE

CALL FILL PF

PRINT 4, lBl FOR~AT (lHl,8A10) TLF=20.·ALOGI0CF)

F=F.l. E06

TO=SECONOfOUH)

XINTZ=AMAX1CXlO·XI,XXZ)

NN=(O-XINTZ)/X!

XINTZ=O-NN·XI

XINTP=XINTZ+NPO·XI

CALL SETFLD

00 = 0

O=XINTP

CALL FIELDS

oKM=0/1 0 0 0 • TIM~=SECONO(oUH)-TO

ATT=A08CFIELo)

IF (ATT .LT. -10.) GO TO 1

AL8=ATT+32.4S+20. 4ALOGI0CoKH)+TLF

FLOS=139.37+TLF-ALB

PRINT 5, OKM,ATT,ALB,FLOS,TIME FORHAT (lX,.OKM=·F8.2,· AOB=·F8.2,· LB=·F8.Z,· FlDS=·F8.Z,

C. TIM~=·F8.2)

O=O+XI

IF (0 .LE. 00) GO TO Z

GO TO 1

END

-109-
CONTINUE

AT S=O

CONTI NUE BEGINNING THE COMPUTATIONS FOR UIN)

Y=FN+XZ

RTX=SQRTIY)

EE ZTA=ZT ABR-HT

COZTA=EEZTA/Y

TAUX=OZTABR-OOZTA

TEHP=.Cj/Y PRF=CISCKBZ·CEEZTA·ODZTA-PHIBR»/(RTX·RTXI)

OPRF=CHPLX(TEMP,K82·TAUX·TAUX)·PRF

EEZTA=ZTABR

OOZTA=EEZTA/Y

TAU=OZTAZ-OOZTA

TAUX=DZTABR-OOZTA

QTEHP(1)=OLTACO)+TAU

QTEHP(2)=CHPLXCTEHP1KB2·TAUX·TAUX)

Q=CHPLXCO.,KBZ·TAU·IAU·Y/FN) CONTINUE

AT S=XCO)

Y=FN

EEZTA=ZTABR-ZTAZ

OOlTA=EEZTA/Y

TAU=OZTAZ-DOZTA

TAUX=OZTABR-DOZTA

TEHP=.S/Y

QTEHP(3)=OLTAIO)+TAU

Q=O+ClCGIQTEHP(3)/QTEHPC1)·RTX/RTCN)/XZ QQ=(SECZ/RTCN»).QTEHPC3).CISCKBZ.(EEZTA.OOZTA-PHIBR+PHIZ)·UZ

B=KB2·TAUX·TAUX

G=IGGI(Q) OG=IGGICQ+CLOGCCHPLXCTEHP,BI/QTEHPCZ»/XZ).CHPlXCTEHP,BI

Q=CMPLXCO.,KBZ·TAU·TAU)+LDUl

00 13001 K=l,Z. TEHP=SQECK)/Y

QTEHP(3)=SQACK)·IGGHCQ+TEHP)

G=G+QTEHPC 3) o~=OG+aTEHP(3)·CHPLX(TEHP,B)

CONTINUE

ZTABR=ZTAIN)

OZTABR=OZTACN)

PHIBR=PHI CN)

SUEROUTINE ADVFLO

COMHON/FIELOO/XI,XHTRHT 10IST,RCVRHT,FREQ,FIELO,XINTZ,XINTP,NLIMIT COMHON/FL01/N,FN,XZ,NP COMHON/FLDZ/K82,HT,RTX fUZTAZ,DZTA(1000) ,OZTA2,ZTAZ,ZTA(1000),PHIZ,PHI(1000),SECZ,

X SEC(1000),RTCI000)

REAL KB2 CO M 0NIF L0 3/GAtot HAtUZ1 U.( 1000) ,L 0UZ, LOU ( 1000) COMPLEX GAHMA,UZ,U,LUUZ.LOU LOGICAL CSGDIF COMHON/FLOS/ZRtSQA(Z),SQE(Z)

COMPLEX G1 DG1PKF,OPRF,Q,QQ,QTEHP COMPLEX Zt<,FIELD CO~PLEX CIS,CEXPtCLOG,IGG,IGGI,IGGH,DLTA

DIMENSION QTEHP(3) DATA CZR=CO.,O.» DATA CSQA=.9082482911·091751709),(SQE=.Z75255128,2.72474487) HERtWITH IS N ADVANCED

N=N+l

FN=FN"+ 1.

CALL ZETA ZTA(N)=ZTAfN-1)+.S·IOZTACN-l)+DZTAIN»

TEMP=.~·OZTACN)·OZTA(N)

PHICN)=PHICN-l)+TEHP+OZTA2

OZTA2=TEHP SECfN)=1.+DZTA2

RT CN) =SQRT CFN)

13001

13000

C

lZ000

C

c

11000

C

c

-110-
14000

C

CONTINUE ITERATING WITH S=X(J), FOR J=l ••• N-Z

J=O

NJ=N

IltOlO J=J+1

NJ=NJ-1

Y=Y-1.

IF(NJ.lE.1) GO TO 15000

EEZTA=ZTABR-ZTAIJ)

OOZTA=EEZTA/Y TAU=OZTA(J)-OOZTA

TAUX=OZTABR-OOZTA QQ=(SEC(J)/RTINJ»·CIS(KBZ·(EEZTA·ODZTA-PHIBR+PHI(J»)·

1 IOLTAIJ)+TAU)·U(J) Q=CHPlX(0 •• K8Z·TAU·TAU)+LOUIJ) B=K9Z·TAUX·TAUX

QTEHP (U =ZR

QT EHP I Z) =ZR

00 IItOll K=1,2 TEI1°=SQE(K)/Y QTEMP(3)=SQA(K)·IGG(Q+TEHP)

QTEHP(1)=QTEHPll)+QTEHP(3) QTEHPIZ)=QTEHPIZ)+QTEHP(3)·CHPlXITEHP.B) 1lt0l1 CONTINUE G=G+QTEHP(1)·QQ

OG=OG-QTEHPIZ)·QQ

GO TO 14010 15000 CONTINUE C AT S=X(N-U TAU=.5·IOZTAIN-l)-OZTAIN»

TEHf=KBZ·TAU·TAU QQ=SECIN-1)·IOLTA(N-1)+TAU)·CIS(-TEHP)·UIN-l)

CAll IGGPUICHPLXIO •• TEHP)+lOUIN-l).QTEHP) QTEHP(1)=QTEHPI1)·QQ

G=G+QTEHP(1) . OG=OG+QTEHP(1)·lOUIN-l)-QQ·QTEHPIZ)

CAT 16000 CONTINUE S= X( N) CAll IGGFIPRF-GAHHA.G.-OPRF-GAHHA·OG.Z./IGAHHA·OlTAIN)·SEC(N». 1 UIN).lOUIN» RETURN

END

-111-
CO~PLEX FUNCTION WERF(ZZZ) COMPLEX Z,ZZZ,ZV,V,Z2,C,H,S OI~ENSION C(12) ,W(5,4). EQUIVALENCE (S,C(12») DATA (C(l) = (.0,-.5641895835») DATA « (W(I,J) ,1=1,5) ,J=1,4)= (1. ,.0) t

X (3.678794411714423E-Ol,6.071577058413937E-Ol), X (1.831563888873418E-02,3.400262170&60662E-Ol),

X (1.234098040866788E-04,2.011573170376004£-01), X (1.1253517~7192646E-07,1.459535899001528E-01),

X (4.27S835761558070E-01,O.OOOooooonOOOOOOE+OO), X (3.047442052569126E-01,2.082189382028316£-01), X (1.40239S813662779E-01,2.222134401798991E-Ol', X (6.5317777289046q7E-02,l.739183154163490~-01),

X (3.62814564S998864E-OZ,1.358389510006551E-Ol),

X (Z.553956763105058E-01,O.OOOOOOOOOOOOOOOE+OO), X (Z.184926152748907E-Ol,9.Z99780939Z6n186E-OZ), X (1.4795275q5120158E-Ol,1.311197170842178~-01),

X (9.271016642644332E-OZ,1.283169622282615E-01),

X (5.~68692961044590E-02,1.132100561244882E-01), X (1.790011511813930E-01,O.OOOOOOOOOOOOOOO~+OO),

X (1.642611363929861E-01,5.019113513524966£-02),

X (1.307574696698522E-01,8.111265047745472E-02), X (g.640250558304439E-02,9.1236326004Z1258E-QZ), X (6.979096164964750E-OZ,8.934000024036461E-02»

XX=REALCZZZ)

YY=AIHAGCZZZ)

X=ABS (XX) Y=ABS (YY) Z=CHPLX(X,Y)

LZZ=O

IF(X.G~.4.5.0R.Y.GE.3.5) GO TO 100

I=X+.5

J=Y+.5 V=CHPLX(FLOAT (I),FLOAT(J» ZV:Z-V C( 2) =H(I+l,J+1) AI=O.

00 10 1=3,12 AI=AI-.5

C(I)=(~·C(I-l)+C(I-2»/AI

1 0 CaNT I NtJE

J=lZ

DO 11 1=2,11 J=J-l

11 S=S·ZV+C(J) 20 IF(YY.GE.O.) GO TO 30

IF (LZ2) Z2,21

21 Z2 = Z·Z

22 S=2.·CEXP(-Z2)-S

IFIXX.GT.O.) S=CONJGCS) GO TO ZOO

30 IFIXX.LT.O.) S=CONJGCS) ZOO WERF=S

RETURN

100 LZ2=1

Z2=Z·Z S = Z.«(O.,O.4613135279)/CZ2 - 0.1901635092) + (O.,O.099Q9Z16168)/ XCZ2 - 1.78449Z7485) + (o.,0.00288389387~8./IZZ - 5.52534374379»

GO TO 20

END

-112-
J=O

NJ=NX

J=J+l

NJ=NJ-l

Y=Y-l. IF(NJ.LE.1) GO TO 25000

EEZTA=ZTA8R-ZTACJ)

OOZTA=EEZTA/Y

TAU=QZTA(J)-ODZTA QQ=CSECCJ)/RTCNJ»).CIS(KBZ1fo«EEZTA.DOZTA-PHIBR+PHIfJ»)·(OLTA(J)+TA

1U)·UfJ)

a=C~PLX(O.~K82·TAU·TAUI+LOU(J)

QTEHP(l)=Zt<

RTX=SQRT(Y)

EEZ1A=ZTABR-HT

OOZTA=EEZTA/Y PRF=CISCK82·(EEZTA·ODZTA-PHIBR»)/CRTX·RTXI)

IFCZ.EQ.O) GO TO 26007

EEZTt=ZTABR

OOZTA=EEZTA/Y

TAU=OZTAZ-OOZTA

aTE~P(1)=OLTA(O)+TAU

a=CHPLX(O.,K82·TAU·TAU~Y/FNX)

CONTINUE

AT S=XCO)

CONTINUE ITERATING WITH S=XfJ), FOR J=1 ••• NX-2

CONTINUE

BEGINNING THE COMPUTATIONS FOR W

CONTINUE

AT 5=0

Y=FNX

EEZTA=ZTABR-ZTAZ

OOZTA=EEZTA/Y

TAU=OZTAZ-ODZTA

QTEtP(3)=OLTA(O)+TAU

a=Q+ClOGCQTEHP(3)/QTEHP(1)·RTX/RT(NX»/XZ aC=(SECZ/RTCNX»1foQTEMP(3).CIS(KBZ1fo(EEZTA.OOZTA-PHIBR+PHIZ»·UZ

G=IGGICQ) Q=CHPLXCO.,KBZ1foTAU1foTAU)+LDUZ

00 23001 K=1 2 G=G+SQA(K)·IGGHCQ+SQE(K)/VJ

CONTINUE

G=G1foOQ

ZTABR=ZTA(NX)+Z

DZTA8R=DZTACNX)

PHIBR=PHI(NX)

SUBROUTINE FIELDS C0H~1 0NI FIEL00 I XI t XMTRHT, 01ST, Rev RHT, FREQ, (;, XINTZ, XI NT P , NLI r'1 I T

CaHH0NI FLO 1/N, FN, XZ, NP toZTAZ , 0 ZTA( 10 00 » ,~

COHHON/FL02/KB2 1HT, RTXI , DZTA2 , ZTAZ, ZTA(1 000) , PHI Z, PHI ( 1000) , SECZ, X SEC(100Q),RT 1000)

REAL K82 COHHOf\/FL03/GAMHA,UZ,U (1000) ,LOUZ,LOUII000) COMPLEX GAHHA,UZtU,LOUZtLOU COHHON/FL05/ZR,S~A(2),S~E(2)

COHPLEX ZR,G,PRF,Q,QQ,QTEHP CO~PLEX CIS,IGG,IGGI,IGGH,OLTA DIHENSION QTEHP(3)THE RECOMMENCEMENT

F NX=NX=( 0 1ST- XI NTZ) IX I + 0• 5

FORHAT (.0 SYSTEM 52 ERROR·) IFCNX.lE.N) GO TO 20001

CALL ADVFLO $ GO TO 20000

CONTINUE

Y=FNX+XZ

x=y·X!

OIST=X

Z=RCVRHT/X!

IF(Z.lT.O.) Z=O.

24010

23001

24000

C

22000

C

23000

C·

C

52

20000

20001

21000

C

-113-
DO 24011 K=1,2 QT£~p(l)=aTC:J-tP(l)+SQA(K)·IGG(a+SQE(K)/Y)

24011 CONTINUE G=G+QTE:HP(l)4-QQ

GO TO 24010

25000

C

26000

C

26008

26007

-114-
COMPUTE PLANE EARTH UCN)

c

8000

52

9000

C

9001

<3002

9080

SUB~OUTINE SETFLO

COH~ON/FIELOO/XI,XMTRHT,DIST,RCVRHT,FREQ,FIELO,XINTZ,XINTP,NLIHIT

COH:iON/FLD1/N,FN,XZ,NP,DZTAZ,DlTAf1000t

COH~ON/Fl02/KB2,HTtRTXI,DZTA2,ZTAl,ZTAfl000),PHIZ,PHI(1000),SECZ,

X SEC(1000),~T(10UO)

REAL K9Z COHHCN/F~D3/GAMHA,UZIU(1000),LOUZ,LOU(1000)

COMPLEX GAHHAiUZ,U,LUUZtLDU CO~MON/FLD4/G CF,BWBG,ABG,BPE,BPE2,RTXl COMPLEX GZCFtBWBG,ABGIBPE,BPE2 COMPLEX APE~U1,a2~Q31U4~Q5,Q6tOLTA COMPLEX WER~,HWERf,C S,~IELO

CONTINUE

HT=Xt1T~HT/XI

KB2=FR~Q·XI/.953688E8

XZ=XINTZ/XI IFIXl.LE.O.) XZ=4. RTX2=S()~T(XZ)

~TXI=Sa~T(XIt NP=HAX1(1.,XINTP/XI-XZ+.5)

IF CNP .GT. NLIHIT) PRINT 52

FORHAT C.O SYSTEM 52 ERROR·)

N=O

FN=O.

CALL SETZTA

ZTAZ=OZTAZ·Xl

OZTAZ=.S·OZTAZ·OZTAZ

SECZ=1.+0ZTAZ PHIZ=Z.1f.COZTAZ·XZ-OZTAZ1f.HT)

Tl=SCRTC.S1f.KBZ)

T2=T11f.HT

APE=CHPLXfTZ,T2)

T2=.56418958·T1

GA~HA=CHPLX(T2,-TZ)

T2=SECZ1f.Tl

CALL SET0 LTA( 0) BPE=CHPLX(TZ,TZ)1f.OLTA(O)

BPEZ=BPE·SPE

ABG=APE/RTXZ 9WBG=8PE1f.WERF(ABG+BPE·RTXZ)

T3=KBZ1f.HT·HT

Q6=Z.·APE1f.BPE

CONT INUE

GO TO 9002

N=N+l

FN=FN+ 1.

OZTA(N)=OZTAZ

lTA(N)=lTACN-l)+OZTAZ

SECCN)=SECZ

PHICN)=PHICN-1)+OZTAZ+OZTA2

RT(N)=SQRT(FN)

Y=FN+Xl

T1=SORTCYt

TZ=T3/Y

01=APE/Tl

QZ=BPE1f.Tl

Q3=01+02

Qlf=HWERF(Q3)

QS=.5/(Q3-Qltt U(N)=CIS(TZ)/C1.+Q2/(Ql-QS')/fTl·RTXI)

lOU(N)=(Q6-QZ·Q4'/(1.-Ql/QS)-CHPlXC.S,TZ»/Y

IFCN.LT.NP) GO TO 9001 GZCF=CHPLX(AIHAG(CIS(T3/XZ».-REAL(CISCT3/XZ»).(SECZ.1.7724538~/

X RTXI)/UZ RETURN

ENO

-115-
5

6

10

11

12

30

CO~PlEX FUNCTION DLTA(J) CO~~O~/FIELOD/XI,XMTRHTtOIST,RCVRHT,FREQtFIElO,XINTZ,XINTP,NLIMIT

CO~~O~.IGROUNOI NGC,OX(SO),EP(SO),SIG(SO) ,IPOL DIMENSION OELTA(SO),JX(SO) COMPLEX OELTA~ETA,FIELO

00 5 I=l,NGC IF (JX(I).GE. J) GO TO 6

CONTINUE

I=~GC OlTA=OELTACI)

~ETURN

ENTRY SETOlTA

00 10 I=l,NGC ETA=CHPLX( EP ( I) t SI G( I ) • • 1795 3E111 FRE Q)

O~LTA(I)=CSQRT(ETA~1.1

JXCI) = (OXII)' - XINTZ)/XI + 0.5

IF (IPOL .NE. 0) OELTA(I)=OELTA(I)/ETA

RETURN

END

SUBROUTINE BINETtXX,AlPHA,XBINET) COMPLEX ALPHAtXBINET

COMPLEX A1 I X, KTI X, KNLtQ,QQ,RTA,IRTPI

COHPLEX Ht.RFfCIS DIMENSION XB NETJ2),KNlC8),Q(Z) DATA (IRTPI=(O.,l.772453851»

x=xx

RTIX=CHPLX(SQRT (.S·X),SQRT (.S·XJI A=ALPHA . IF(AMAX1(ABSCREALCA»,ABS(AIMAGCA)).GT•• 3542) GO TO 30

IX=CHPLXCO.,X)

QQ=CISeX)

KNl(1)=IRTPI·QQ·WERF(RTIX)/RTIX

FK=-.5

00 11 K= 2,8 FK=FK+ 1.

KNLIK)=CQQ+IX·KNLCK-1)/FK

FK=7.

KK=8

Q(1)=KNLCKKJ

Q(ZJ=KNL(KK-1)

DO 12 K=1,6

KK=KK-l

FK=FK-l. QQ=A/FK

Q(1)=KNlCKKJ-QC1)·QQ

Q(2)=KNLCKK-l)-QC2)·QQ

XBINET(I)=Q(l)

XBINET(Z)=Q(Z)

RETURN

CONT INUE

QQ=CEXPtCHPLXC-.IZ07822376,X+1.570796327)-A)

RTA=CSQRT(-AI

Qfl)=WERFtRTIX+RTA)

-o( 2) =WERF(RTIX-RTA) XBINET(l)=QQ·(QCZ)-Q(l»/RTA

XBINETCZ)=QQ·(QCZ)+Q(I)t/RTIX

RETURN

ENO

-116-
10

11

12

13

20

21

22

30

.. 0

61

62

100

111

110

101

102

SU3ROUTINE ZETA CO~MON IPROFILEI GE,NPF,PFX(SOO),PFZ(SOO) COHHON/FL01/N,FN,XZ.NP,DZTAZ,OZTA(1000)

COMHON/FIELOO/XI,XXX(9)

K=KA

HZO=HZl S HZ1=O.

IF(.N-NN)10,20 ,30._ . ·1- 8=84 $ XB=XA=XA+X

Ul=-XI

GO TO 101 HZ1=e(B·U·3.+A)·Z+IY·B+U·AJ·O.S·OZ)·V+HZl

IFeXl .IT. XB)100,12 IF(e)40,40,13 B=-BA S KA=K $ XB=XB+XI

GO TO 102 XB=XA=PFX(NPF)

Ul=-xI·l.5 ASSIGN 21 TO lS _ .. S .. _GO TO 101

HZ1=(CZ-PFZCNPF»)·U+Y·OZ/6.)·V·O.5+HZl

IF(xt .IT. XB)100,22 B=HZ1·SA/O.5625

HZ1=-S·O.5+PFZINPF)

GO TO ltO

HZ1=HZO+B

OE=OE-OOE OZTACN)=(HZ1-HZO)/XI+OE

RETURN

ENTRY SETZTA

K=l

HZO=PFZ(lt

HZ1=Ul=XA=O.

XB=fXZ+NP+O.5)·XI

ASSIGN 61 TO lS $ GO TO 100

HZ1=I(Z-PFZ(1»)·U+Y·DZ/6.)·V·O.5+HZl

IF(X1 .IT. XB)100,6Z XA=XB-XI·O.5

OOE=GE·XI

DE= ((PFXCNPF)+XA··Z/PFX(NPF»·O.5-XA)·GE

HZ1=HZ1·3./XB··Z

DZTAZ=HZ1/XB+DE

HZ1=HZ1+PFZ(1)

XA=XB

KA=K A=2./XI

BA=A·O.Z5/XI

NN=PFX(NPF)/XI-XZ-O.5

ASSIGN 11 TO lS

RETURN

CONTINUE

IF(K.NE. NPF)1101111 Xl=XB S GO '0 102

K=K+l

CONTINUE

Xl=PFX(K)

V=XI-PFXCK-l. S U=XI-XA Z=(V-U)·PFZIK)+U·PFZ(K-IJ)/V

OZ=(PFZ(K)-~FZ(K-l»/V

CONTINUE

UO=Ul

Ul=AHINlCXltXBJ-XA

U=Ul+UO V=Ul-UO

Y=U·U·3.+V·V

GO TO LS.Cl1,21,61J

END

-117-
1

2

1002

1006

3

100..

6

7

9

1005

a

1001

1003

SUB~OUTINE FIll PF COMMON/FIElOO/XI,HTA,O,HTB,FHHZ,FlO,XINTZ,XINTP,NLIMIT

COHPLEX FL0 CO~HCN IPROFIlEI GE,NPF,PFX(500),PFZ(SOO) COMMON IGROUNDI NGC,DXeSOt,EP(SO),SIG(SO),IPOL,SF COHHON IHEADI lBl(8) OIH~NSION LPOL(Z) S OATAflPOL=4HHORZ,4HVERT)

READ 1001tLBL

IFCEOF(SLINPUTJ) 1,2 STOP

CONTINUE READ 10021 NPF,IXU,IZU,SF' FORHAT 13 10,FiO.0) IF (~PF .LE. SOD) GO TO 3

PRINT 1006 FORHAT CIII.OTROUBLE WITH ARRAY FOR PROFILE OR GROUNO CONSTANTS·)

STOP

CONTINUE READ 1004, (PFX(J),PFZ(J), J=l,NPF) FORHAT (4(FiO.2,FiO.O» XK=1000. IF (IXU .EQ. 1) XK=1609.3

00 It I=l,NPF PFXCI'=PFXCI)·XK

IF CIZU .EO. 0) GO TO 7

DO & I=l,NPF PFZII)=PFZIIJ·.3048

CONTINUE . REAQ 1003,HTA%HTB,FHHZ,ENO,IPOL READ i002, NGl,; IF CNGC .lE. 50) GO TO 9

PRINT 1006

STOP

CONTINUE READ 1005t (OXII), SIGfI),EPfI), I=l,NGC) FORHAT 14(F7.0,F7.4,F&.0» .

g~(~);O~l~r~1000. O=PFXINPF)

ANT=(PFZC1)+PFZeNPF»/2.

ENS=EN O·EXP(-1. 057 E- O..·ANTJ

GE= Cl.-0.0466S·EXPCO.00S571·ENS)/6370.E03 IFf END .EO. 0.) GE=O.

RETURN FORHAT e8A10) FORHAT ( ..F10.O,I3)

END

COMPLEX FUNCTION CIS(X) CIS=CHPLXCCOS(X),SIN(X»

RETURN

END

-118-
INTEGER FUNCTION CSGDIFCZ1,ZZ) COfJPlEX Z1,l2 ABN(l)=ABS (REAL(Z»+ABS (AIHAG(Z»

CSGOIF=1 IF(AEN(Zl-ZZ) .LE. ABN(Z2)·O.5E-OS)

RETURN

END

CSGDIF=O

1

2

3

1

2

COMPLEX FUNCTION IGGCALPHA) COMPLEX ALPHA

COMPLEX A,IPI,PSINH OIM~NSION A(3) DATA (IPI=(O.,3.1~15qZ654»,(SQPI=q.86q604401)

A(1)=ALPHA

A(Z)=AC1)-IPI

A(3)=A(1)+IPI

T=AIHAG(A(l)1

IF(T.GT.2.) GO TO 2

IFCY.LT.-2.) GO TO 3 IGG=SQPI·PSINHCA(1»/CACZ)·A(3»

RETURN IGG=-SQPI·PSINHCA(Z»/IAC3)·AC1»

RETURN IGG=-SQPI·PSINH(A(3»/CAC1)·ACZ)

RETURN

END

COMPLEX FUNCTION IGGHCALPHA) COMPLEX ALPHA

COMPLEX A,B,IPI,PSINH OIH~NSION A(3) DATA CIPI=IO.,3.141592654»,CSQPIB2=4.934802201) A(1)=ALPHA

A(Z)=AC1)-IPI

A(3)=A(1)+IPI

T=AIHAGCA(1)t

IFCT.GT.2.) GO TO 2

IFCT.LT.-2.) GO TO 3

8=.5·A(1)

I GGH=(S QPI B2. CEX,P ( B) • PSI NH ( B J - A ( 1 ) ) / (A (2 »• A C3» » RETJRN

B=.5·A(2) . IGGH=-(SQPIB2·CEXPCB)·PSINHCB)/A(3)+1.)/A(1)

RETURN

B=.5·AC3.

IGGH=-CSQPIB2·CEXPCB)·PSINHCBJ/ACZ)+1.J/AC1)

RETU~N

END

-119-
COMPLEX tlHJCTION IGGI (ALPHA) COMPLEX ALPHA,WERF CO~HON/FLD4/GZCF9BWBG,ABG,BPE,BPE2,RTXZ

CO~PLEX GZCF,8WBG,ABG,BPE,BPE2 COMPLEX A,AA,AAX . A=ALPHA

AA=CSQRTCA)

AAX= AA· R. TXl IGGI=GZCF·(aWBG/(BPEZ~A)-.5·(WERF(AaG+AAX)/(aPE·AA)+WERF(ABG-AAXl/

X tBPEtAA)) RETURN

END.

SU9~QUTINE IGGPU(ALPHA,XIGGPU) COMPLEX ALPHA,XIGGPU COMPLEX SHERF

CQ.... MP.LEX .A... ,B.iQ.·.l.IT.PI,IH.PI OIHENSIONXGGPUlZ),Qf3)

DATA (ITPI=(O.,6.283195307»,(IHPI:(O.,1.57Q196327» A=AlPHA 8=A+A . . A=.701106781Z 4 CEXP (- A) Q (1) :;:'SHERF (B) Q(Z)=SHERF(B+ITPI)

Q(3)=SHERFfB-ITPI)

XIGGPU(1)=A4CQ(1)-O.,4fQ(Z)+QC3)))

XIGGPU(2)=IHPI4A 4CQ(Z)-Q(3»

RETURN . END

su.e~OU.. TINE. IGGUC.A.L.PHA.,.XIGGU) COMPLEX ALPHA,XIGGUl4, COMPLEX A,Q(6) COMPLEX IPI,IHPI DATA (IPI:(O.,3.1415926541),CIHPI=(D.,t.57079&327») A:::ALPHA . CALL SHERFPfA,Q(l) CALL SHERFPlA+IPI,Q(3» . CALL SHERFPfA·IPI,Q(5)) XIGGU(1)=Q(11-0.S·CQ(3)+Q(§»)

XIGGU(Z);IHPt 4 j Q( S ) - QC3 ) ) XIGGU(!)=Q(Z)-O.5·CQ(4)+Q(o»

XIGGU(~)=IHPI·(Q(&)-Qr4).

RETURN

END

-120-
100

52

101

102

103

10'+

105

106

107

108

110

SUBROUTINE IGGFCAA,BB,CC,U,LDU) COMPLEX AA,BB,CC,U,LDU COMPLEX A,C,O,Zl,Z2,W,OH,GO,XG(4),Q(31 DATA(E=t.E-04),(RO=3·)1(KTO=100)

ABNfZJ=ABS (REAL(Z»+A~S (AIHAGCZ» A=AA $ C=CC

KT=D

Z1=0=8 el A IFCREALIZ1) .IT. -ZO.) Zl=CHPLXC-20.,AIHAG(Zl») fA=1. s TB=Z.

R2=1.E300 KT=KT+l $ IF(KT .EQ. KTO) PRINT 52

FORHAT (·0 SYSTEH SZ ERROR·) CALL IGGUCZ1,XG) Q(1)=CEXPC-Zl·0.S)

aC2) =C IQ (1) Q(3)=XG(1)·U(1)+Q(Z)

W=CZI-Q)·QC3)+XGCZ)·Q(1)

Rl=ABNCW)

IFCR1.TB .lE. R2)10Z,101 TA=TA·O.5

TB=EXPITA·O.693)

GO TO 108

Z2= 21

RZ=Rl OW=(Zl-0)·(XG(3)·Q(1)+QCZ»+XGC4)·Q(1)-W·O.5+QC3)

GO=H/OW

T=ABNCGO) IFeT .LE. CABNCZ1)+Q.Ol)·E' GOTO 110

IFCTA-l.)103,106,104

IF(TA-D.5)105,104tlD~

TA=t. S T8=2. S GO TO 10&

TA=TA·Z.

TB=EXPCTA·0.(93)

IFCT·TA .LE. RO)108,101 TA=RO/T

TB=EXP(TA·O.&93)

Zl=ZZ-GO·TA

GO TO 100

LOU= Zl=ZZ-GD

CALL IGGUCZI1XG) U=A/(XG(l)/(~EXP(Zl)·C)+l.)

RETURN

END

SUBROUTINE IGZPUCX~ALPHA9XIGZPU) COMPLEX ALPHA,XIGZpU COHPLEX A,B,Ql,QZ9Q3.ITPI DIMENSION XIGZPUIZ),Q1IZ)tQ2CZ),Q3(Z) DATA (ITPI=(O.,6.Z6318530~» y=.s"'x

A=ALPHA

B=A+A

A=CEXP(A)·.701106781Z

CALL BINETfY,B,Ql) CAll BINETfY,B+ITPI,QZ) CAll BINETfY B-ITPI,Q31 XIGZPU(1):A·tOl(1)-.S·CQ2(1)+Q3(lJ»)

XIGZPUCZ)=.S·A·CQ1(2)-.S·(QZC2)+Q3C2»)

RETURN

END

-121-
30

10

11

12

13

sue~OUTINE IGZU(XiALPHA,XIGZU) COMPLEX ALPHA,XIG U

COMPLEX A,Ql,QZ,Q3,IPI OI"';:NSION XIG LU(Z) ,Q1(Z) ,OZ(2) ,Q3(2) DATA fIPI=(O.,3.1~lS9205~))

Y=X

A= ALPHA CALL BINET(y,A,Ql) CALL BINET(Y,A.IPI,QZ) CALL BINET(Y,A-IPI,Q3)

00 30 K=1,2 XIGZU(K)=.S·Ql(K)+.ZS·(QZ(K)+Q3(K»

RETURN

END

COMPLEX FUNCTION PSINHCZZI

COMPLEX ZZ,l,V

Z= Zl IFfABSfREALCZ»)+ABS(AIHAG(Z».GT.l.J GO TO 10

Z=Z·Z PSINH=I.+Z·(.166666&7+Z·(.83333333E-Z+Z·(.19841270E-3+

X Z•• 275 ~7319E-5»)

RETURN Y=CEXPCZ) PSINH=fY-l./Y)/(Z+l)

RETURN

END

COMPLEX FUNCTION SHERFCZZ) COMPLEX l,Zl,Y COMPLEX WERF

81~~N~~~~.~t~~~~~t~~~~4'.1Z6Zq345q6E-3 .9472009472£-3

X .6156806157E-2,.3386243386E-l,.1523~09524,.5333333J33, X 1.333333333,2 •• ,CCFK=.0009683,.01486,.06198,.1520,.2842,.453~,

X .6543,,6810) Z=ZZ T=AHAX1(ABS CREALCZII,ABS CAIHAGCZIJ) 00 11 1(=1,8 IFCT.LT.CFKCK» GO TO 12

CONTINUE

Y=CSQRT (Z» SHERF=1.7724S38S·CCEXPCZ)-WERFCCHPLXC-AIHAGCY),REALCY)»)/y RETURN . J=10-K SHERF=CHPLXCCFfJ-l),O.)

~~E~~=~H~R~.Z+CFCK) . ~ETURN

END

-122-
SUg~OUT I i~E SH ERF P (ZZ, XSH) CO~PLEX ZZ,XSH(Zt . COMPLEX Z,Y,XS(Z)1 HERF DIM~NSION CF(9),CtP(9),CFKC8) DATA (CF=.1485805401E-4,.12&2934596E-3,.9~7Z009412E-3,

X .6156806151E-2,.3386243386E-1,.1523809524,.5333333333, X 1.333333333,Z.),CCFK=.0009683,.0148o,.06198,.1520,.2842,.4534,

X .6543,.8810) DATACCFP=.140760S12E-4,.118864433E-3,.8840S4217E-3,

1 .568320568£-2,.0301840308,.135449735,.451142857,

2 1.06&6&6667,1.333333333)

Z=ZZ T=AMAXICABS CREALCZI),ABS (AIMAGCZ»))

00 11 K=1,18 IFCT.LT.CfKfK) GO TO 12

11 CONT INUE . Y=CSQRTCZ) XS(1)=1.17Z4538S·(CEXPCZI-WERF(CMPLXC-AIHAGCY),REALCY) » ) / Y XSCZ)=C(Z-O.5)·XSI1)+1.)/Z

GO TO 20

12 J=10-K XSfl)=CHPLXCCFCJ-l),D.)

XS(2)=CHPLXfCFPfJ-l),O.)

00 13 K=Jt 9 XS(lJ=XSC1)·Z+CFCK) 13 XS(2)=XS(2)·Z+CFPCK) 20 XSH(1)=XSC1)

XSHCZI=XSCZ)

END

COMPLEX FUNCTION HWERFCZZ) CO~PlEX ZZ,Z,WERF Z=ll

IF CAIHAGCZ) .IT. O••OR. (ABSCREALCZ».LT. 6 •• ANO. AIHAGCZ) .IT.

C 6.») GO TO 10 HWERF=1./CZ-l.5/(Z-2./Z»

RETURN 10 HWERF=Z-.5/CZ+CO.,-.56418958)/WERFCZ»

END

-123-
HOOD

C

CONTINUE ITERATING WITH S=X(J). FOR J=1 ••• N-Z

14010

14011

16000

C

15000

C

J=o

NJ=N J=J+1

NJ=NJ-1

Y=Y-1.

IF(NJ.lE.l) GO TO 15000

EEZTA=ZTABR-ZTA(J)

00 ZTA=EEZTA/Y TAU=OZTA(J)-OOZTA

TAUX=OZTABR-OOZTA

QQ=lSEC(J)/RTlNJ»·CISlKBZ·(EEZTA·OOZTA-PHIBR+PHI(J»). 1 (OlTAlJ)+TAU).U(J) Q=CHPLX(O •• KBZ·TAU·TAU)+LOUIJ) B=KBZ·TAUX·TAUX

QTEMP (U =ZR

QTEMP( Z)=ZR

00 14011 K=1. Z TEHI'=SQE(K)/Y

QTEMP(3)=SQAlK)·IGGlQ+TEMP)

QTEHP(1)=QTEMP(1)+QTEMP(3)

QTEHP(Z)=QTEHP(Z)+QTEMP(3)·CHPLXlTEMP.B)

CONTINUE

G=G+QTEHP U) "'QQ OG=DG-QTEHPlZ)·QQ

GO TO 14010

CONTINUE

AT S=X(N-t) TAU=.5"lOZTA(N-1)-OZTAlN»

TEHt=KBZ·TAU·TAU

QQ=SEC(N-l)"'lOlTA(N-1)+TAU)·CIS(-TEMP)·UlN-1)

CALL IGGPUlCMPLXCO. tTEHP)+LOUCN-1).QTEHP) QTEMPll)=QTEHP(1)"'Qy

G=G+QTEHPU)

OG=OG+QTEHP(1)·lOUlN-1)-QQ·QTEMPlZ) CONTINUE

AT S=XlN) CALL IGGFCPRF-GAHMA·G.-OPRF-GAHMA·OG.Z./lGAHHA·OLTAIN).SEClN», 1 UlN).lOUlN» RETURN

END

-124-
~~ EV..0 A, F=2.0 ~1HZ , HA=HAR=D., PROGRAM INTEQ

DKH= .51 ADS: -5.68 LB= 26.94 FLOS= 118.45 TIME: .00

OKM= .61 ADa= -5.4& LB= 28.71 FLDS= 116.&8 TIME= .02

OKH= .71 ADS: -5.53 LB= 29.97 FLOS= 115.42 TIME= .05

OKH= .81 ADS: -5.55 L8= 31.09 FLOS= 11"4.30 TIME= • 0&

OKM= .91 ADS= -5.51 LB=. 32.14 FLDS= 113.25 TIME= .08

OKM= 1.01 ADS= -5.44 LB= 33.12 FLDS= 112.27 TIME= .10

OKH= 1.11 ADS= -5.38 LS= 34.00 FLOS= 111.39 TIME= .12

OKM= 1.21 ADS= -5.25 LB= 34.88 FLOS: 110.51 TIME= •1,.

OKH= 1.31 AD8= -5.15 LS= 35.66 FLOS= 109.73 TIME= .17

OKH= 1.41 ADS= -5.07 LB= 36.38 FLDS= 109.01 TIME= .19

OKH= 1.51 ADS= -5.25 LB= 36.80 FLDS= 108.59 TIME::. .21

OKH= 1.61 ADS= -5.2" L8= 37.37 FLDS= 1 08. 02 TIME= .2,.

OKH= 1.71 ADS= -5.00 LB= 38.13 FLOS= 107.26 TIME= .27

OKH= 1.81 AD8= -4.85 L8= 38.78 FLDS= 106.&2 TIME= .29

OKM= 1.91 ADS= -4.73 LB= 39.36 FLDS= 106.03 TIME= .32

OKH= 2.01 ADS= -4.82 LB= 39.71 FLOS= 105.68 TIME= .35

OKH= 2.11 ADS= -4.99 LB= 39.97 FLOS= 105.,.2 TIME= .38

OKH= 2.21 ADS: -5.12 La= 40 •.23 FLDS= 1 05.16 TIME= .41

OKH= 2.31 ADS: -4.90 LB= ltO.84 FLOS= 104.55 TIME= .43

OKH= 2.41 ADS: -4."0 LB= 41.71 FLOS= 103.68 TIME= .46

OKH= 2.51 ADS: -4.lt5 LB: 42.02 FLDS= 103.38 TIME= .49

OKH= 2.61 ADS= -4.83 LB= Itl.97 FLDS: 103.,.2 TIME= .52

OKH= 2.71 ADS= -5.01 LB~ ..2.12 FLOS= 103.27 TIME= .55

DKH= 2.81 ADB= -5.11 LB= 42.33 FLDS= 103.06 TIME= .58

OKH= 2.91 ADB= -5.00 LB: 42.74 FLOS= 102.65 TIME= .60

OKM: 3.01 ADB= -4.87 LB= "3.17 FLDS= 102.22 TIME= .63

OKH= 3.11 ADS= -,..71t LB= ,.3.59 FLOS= 101.80 TIME= .66

OKH:;: 3.21 ADS: -4.62 LB= 43.98 FLDS= 101.1+1 TIME= .&9

OKH= 3.31 ADS: -4.65 LS: 44.22 FLOS= 101.18 TIME= .72

DKH= 3.41 AOB= -4.72 LB= 44.41 FLDS= 1 00. 98 TIME= .75

OKH: 3.51 ADB= -4.57 LB= 41t.81 FLDS= 100.59 TIME= .78

OKH= 3.61 AOB= -4.ltl LB= 45.21 FLDS= 100.18 TIME: .81

OKH: 3.71 ADS= -5.41 La= 41+.45 FLOS: 100.94 TIME: .85

OKH= 3.81 AOB:: -6.64 LB: 43.lt5 FLOS= 101~94 TIHE= .88

OKH=' 3.91 ADS= -5.58 LB: 4,..74 FLOS= 100.65 TIHE= .91

OKH: 4.01 ADS= -4.48 LB= 1+6.05 FLOS= 99.31t TIHE= .9"

OKH= 4.11 ADS= -4.52 La= 46.23 FLDS= 99.16 TIME= .98

OKH= 4.21 ADB= -4.48 LB= 46.47 FLDS= 98.92 TIME= 1.01

OKH= 1t.31 AOS= .3,. LB= 51.50 FLOS= 93.89 TIHE= 1.04

OKM= ... "I" ADS::=: 3. It 7 LB= 54.83 FLOS= 90.5& TIHE= 1. 08

DKH= 4.51 ADe= 5.13 LB= 56.68 FLDS= 88.71 TIME= 1.12

OKH= 1t.61 ADS= 7.11 La= 58.86 FLDS= 86.53 TIHE= 1.1&

OK": It.71 ADS: 8.08 LB= 60.01 FLDS= 85.38 TIHE= 1.19

OKH= ".81 ADS= 8.85 LB= 60.96 FLDS= 81+.1+3 TIHE= 1.23

OKH= 4.91 ADS: 6.93 LB= 59.23 FLOS= 86.1& TIHE= l.l7

OKH= 5.01 AOB= 6.28 LB: 58.74 FLDS= 86.&5 TIHE= 1.32

OKH= 5.11 ADB:; 5.23 LS= 57.81 FLDS= 87.52 TIHE= 1.35

OKH: 5.21 ADB= 9.68 LB: 62.49 FLOS= 82.90 TIME= 1.39

OKH= 5.31 ADB:: 12.65 LB: 65.62 FLOS= 79.77 TIHE= 1.44

OKH= 5.41 ADS= 11.55 lB~ 6".68 FLOS= 80.71 TIHE= 1.48

OKH= 5.51 ADS= 15.89 LB= 69.18 FLDS= 76.21 TIHE= 1.56

OKH: 5.61 ADS: 13.92 LB= 67.37 FLOS= 78.02 TIME= 1.61

-125-
OKH= 5.71 AOB= 11.49 L8= 65.09 FLOS= 80.30 TIME= 1.66

OKH= 5.81 AOB= 8.63 LB= 62.39 FLOS= 83.00 TIME= 1.70

OKH= 5.91 AOB= 8.83 LB= 62.73 FLOS= 82.6& TIME= 1.75

OKH= 6.01 AOB= 10.29 L8= 64.31+ FLOS= 81.05 TIME= 1.60

OKH= 6.11 AOB= 12.08 LB=· 66.27- FLOS= 79.12 TIME= 1.65

OKH= 6.21 AOB= 11.99 LB= 66.32 FLOS= 79.07 TIME= 1.89

OKH= 6.31 ADB= 11.11

1

LB= 65.58 FLOS= 79.81 TIME= 1.94

OKH= 6.41 AOB= ·10.60 LB= 65.21 FLOS= 80.18 TIME= 2. 00

OKH= 6.51 AOB= 9.11 L8= 63.85 FLOS= 81.5" TIHE= 2.04

OKH= 6.61 AOB= 7.44 LB= 62.32 FLOS= 83.07 TIME= 2.09

OKH= 6.71 ADB~ 8_.70 LB= 63.70 FLDS= 81.fi9. TIME= 2.14

OKH: 6.81 ADB= 8.10 L8= 63.23 FLOS= 82.16 TIME= 2. 19

OKH= 6.91 AOB= 6.62 LB= 61.88 FLOS= 83.52 TIME= 2.24

DKH= 7.01 ADB= 5.62 LB= 61.00 FLOS= 84.,39 TIME= 2.29

OKH= 7.11 AOB= 4.88 LB= 60.39 FLOS= 85.-'0

a TIME= 2.3 ..

OKH= 1.21 AOB= 4.28 LB= 59.91 FLDS= 85.1+8 TIME= 2.39

OKH= 7.31 AOB= 3.89 LB= 59.64 FLOS= 85.75 TIME= 2.ftS

OKH= 7."1 ADB= 3."8 LB= 59.34 FLOS= 86.05 TIHE= 2.49

OKH= 1.51 ADB= 3.89 LB= 59.87 FLOS= 85.52 TIME= 2.55

OKH= 1.61 AOB= 9.57 LB= 65.&7 FLOS= 79.72 TIME= 2.61

OKH= 1.71 ADB= 13.32 L8= 69.53 FLOS= 75.86 TIME= 2.&7

OKH= 1.81 AOB= 15.77 LB= 72.09 FLOS= 73.30 TIHE: 2.73

OKH= 1.91 AOB= 16.97 LB= 73.40 FLOS= 71.99 TIME= 2.80

OKH= 8.01 A08= 18.30 LB= 74.84 FLOS= 70.55

. TIME= 2.8&

OKH= 8.11 AOB= 17.37 LB= 74.02 FLOS= 71.37 TIME= 2.91

OKH= 8.21 ADB= 16.1t" LB= 73.19 FLDS= 72.20 TIME= 2.97

OKH= 8.31 ADB= 18.58 LB= 75 ....

5 FLOS= 69.95 TIME= 3.02

OKH= 8.41 AOB= 21.63 LB= 78.&0 FLOS= 66.79 TIHE= 3.08

oKH= 8.51 AoB= 24.29 LB= 81.36 FLOS=

6... 03 TIME= 3.1"

OKH= 8.&1 AOB= 21.34 L8= 78.51 FLOS= 66.88 TIME= 3.19

oKH= 8.71 AoB= 18.8ft LB= 76.11 FLOS= 69.28 TIHE= 3.24

OKH= 8.81 AOB= 23.44 LB= 80.81 FLOS= 64.58 TIME= 3.30

OKH= 8.91 ADB= 32.12 LB= 89.59 FLOS= 55.80 TIHE= 3.3&

OKH= 9.01 AOB= 28.18 L"e= 85.74 FLOS= 59.65 TIHE= 3.42

OKH= 9.11 ADB= 25.18 LB= 82.8 .. FLDS= 62.55 TIHE= 3."9

OKH: 9.21 -AOB= 24.23 LB= 81.99 FLOS= 63.a.O TIHE= 3.55

OKH= 9.31 AoB= 22.50 La= 80.35 FLOS= 65.04 TIHE= 3.61

OKH= 9.41 AOB= 23.5& LB= 81.51 FLOS= 63.88 TIME= 3.&1

oKH= 9.51 AOB= 26.02 La= 8ft.05 FLOS= 61.3" TIME= 3.72

oKH= 9.&1 AOB= 27.7" LB= 85.86 FLOS= 59.53 TIHE= 3.78

oKH= 9.71 AOB= 28.13 LB= 86.34 FLDS= 59.05 TIHE= 3.8"

OKH= 9.81 ADB= 34.81 LB= 93.11 FLOS= 52.28 TIHE= 3.91

OKH= 9.91 ADB= 33.61 LB= 92.01 FLDS= 53.39 TIHE= 3.98

OKH= 10.01 AOB= 32.08 LB= 90.5& FLOS= 54.83 TIHE= 4.05

OKH= 10.11 AOB= 29.91 La= 88."7 FLOS= 5&.92 TIHE= 4.13

OKH= 10.21 ADB= 26.12 LB= 84.77 FLOS= 60.62 TIHE= 4.20

OKH= 10.31 ADB= 24.58 La= 83.31 FLOS= 62.08 TIHE= ".21

OKH= 10.,.1 AOB= 23.0,. LB= 81.86 FLOS= 63.53 TIHE= ".34

OKH= 10.51 AOB= 23.03 LB= 81.94 FLOS= 63.Rt6 TIHE= .....

1

OK"= 10.&1 AOB= 23.17 LB= 82.1& FLoS= 63.23 TIHE= .....

9

OK"= 10.71 AOB= 23.72 LB= 82.78 FLOS= 62.61 TIHE= ".5&

OKH= 10.81 AOB= 23.75 LB= 82.90 FLDS= "62.,.9 TIHE= 4.64

°OKH= 10.91 AOB= 23.51 L8= 82.79 FLOS= 62.60 TIME= 4.71

-126-
OK~= 11.01 ADS= 22.83 LB= 82.14 FLDS= 63.25 TIME= 4.78

OKM= 11.11 ADS= 22.28 La= 81.&6 FLOS= 63.73 TIME= 4.83

OKH= 11.21 AD8= 22.35 LB= 81.82 FLDS= 63.57 TIME= 4.90

OKM= 11.31 ADS= 22.10 L8= 81.64 FLDS= 63.75 TIME= 4.98

OKM= 11.41 ADS= 21.12 L8= 80.74 FLOS= 64.65 TIME= 5.05

OKM= 11.51 ADS= 21.78 LB= 81.ft7 FLOS= 63.92 TIME= 5.13

OKM= 11.61 AD8:: 23.31 LB= 83.08 FLOS= 62.31 TIME= 5.20

DKH= 11.71 ADS= 23.9& L8= 83.80 FLDS= 61.59 TIME= 5.28

OKH= 11.81 ADa= 23.58 L8= 83.50 FLOS= 61.89 TIME= 5.35

DKH= 11.91 ADS= 22.7ft L8= 82.73 FLOS= 62.6& TIME= 5.43

OKH= 12.01 ADS= 2Z.56 L8= 82.62 FLOS= 62.77 TIME= 5.49

DKH= 12.11 ADS= 22.58 L8= 82.71 FLDS= 62.68 TIME= 5.58

OKM= 12.21 ADS= 22.59 LB= 82.80 FlOS= 62.59 TIME= 5.65

OKM= 12.31 ADS= 22.61 L8= 82.89 FLDS= 62.50 TIME= 5.72

OKH= 12.41 ADS= 22.64 L8= 82.98 FLDS= 62.41 TIME= 5.78

OKH= 12.51 ADS= 22.66 LB= 83.08 FLOS= 62.31 TIME= 5.86

OKM= 12.61 ADS= 22.70 LB= 83.18 FLOS= 62.21 TIME= 5.94

OKM= 12.11 ADS= 22.59 LB= 83.15 FlDS= 62.24 TIHE= 6.02

DKH= 12.81 ADS= 22.48 L8= 83.10 FLOS= 62.29 TIME= 6.10

OKH= 12.91 ADa= 22.47 L8= 83.16 FLDS= 62.23 TIME= 6.18

OKH= 13.01 ADS= 22.61 LB= 83.36 FLOS= 62.03 TIME= 6.26

OKH= 13.11 ADS= 22.67 LA= 83.49 FLOS= 6t.QO -TIME= 6.33

OKH= 13.21 ADB= 22.67 LB= 83.56 FLOS= 61.84 TIME= 6.41

OKM= 13.31 ADa= 22.78 LB= 83.73 FLDS= 61.66 TIME= 6.49

OKH= 13.41 ADS= 2-2.89 L8= 83.91 FLDS= 61.ft8 TIME= 6.57

OKH= 13.51 ADa= 22.57 LB= 83.65 FLDS= 61.74 TIME= 6.65

OKM= 13.61 ADS= 22.40 LB= 83.55 FLDS= 61.84 TIME= 6.73

OKH= 13.71 ADS= 22.42 LB= 83.64 FLOS= 61.75 TIME= 6.81

OKH= 13.81 ADS: 22.28 LB= 83.55 FLDS= 61.8ft TIME= 6.89

DKH= 13.91 ADS= 22.50 LB= 83.84 FLDS= 61.55 TIME= 6.97

OKM= 14.01 ADS= 22.72 L8= 84.12 FLOS= 61.27 TIME= 7.05

OKH= 14.11 ADS= 22.28 LB= 83.74 FLD~= 61.65 TIME= 7.13

DKM= 14.21 ADS= 22.25 LB= 83.78 FLDS= 61.61 TtHE= 7.22

OKH= 14.31 ADS= 22.30 L8= 83.89 FLDS= 61.51 TIME= 7.30

OKH= 1ft.41 ADS= 21.91 LB= 83.56 FLOS= 61.83 TIME= 1.38

OKH= 14.51 ADS= 21.72- LB= 83.42 FLOS= 61.97 TIME= 7.4&

OKH= 1ft.61 ADS= 20.29 LB= 82.06 FLDS': 63.33 TIME= 1.55

OKH= 14.11 ADS: 18.77 LS= 80.59 FLDS= 6ft.80 TIME= 1.63

OKH= 14.81 ADS= 20.54 LB= 82.42 FLOS= -62.97 TIME= 7.72

OKH= 14.91 ADS= 22.15 LB= 84.09 FLOS= 61.30 TIME= 7.81

DKH= 15.01 ADB= 23.19 LB= 85.18 FLDS= 60.21 TIHE= 7.89

OKH= 15.'11 ADB= 23.79 LB= 85.85 FLDS= 59.54 TIME= 7.91

-127-

FORM OT·29 (3-73)

U.S. DEPARTMENT OF COMMERCE OFFICE OF TELECOMMUNICATIONS

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NO.2. Gov't Accession No.3. Recipient's Accession No.

NTIA Report 79-20

4. TITLE AND SUBTITLE

Ground Wave Propagation Over Irregular, Inhomogeneous

Terrain: Comparisons of Calculations and Measurements.

5. Publication Date

1'1ay 1979

6. Performing Organization Code

NTIA!ITS

7. AUTHOR(S) 9. Project/Task/Work Unit No.

R.H.Ott, L.E.Voqler, and G.A.Hufford

8. PERFORMING ORGANIZATION NAME AND ADDRESS

U. S. Departrrent of Conmerce

National Telecorrmunications and Infonnation Administratibtt. Contract/Grant No.

Institute for Teleconmunication Sciences

325 Broadway, Boulder, Colorado 80303

11. Sponsoring Organization Name and Address 12. Type of Report and Period Covered

Electromagnetic Compatibility Analysis Ceni;er

North Severn, Annapo.l.i.s , Maryland 21402 and

Dept. of Air Force, Space & Missile Systems Org. (AFSC) 13.

Bldg. 523, Rrn. 303, rbrton AFB, CA 92409

14. SUPPLEMENTARY NOTES

15. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography ot literature survey, mention it here.)

An algorithIn (PROGRAM. WAGNER) that evaluates HF ground-wave attenuation over

irregular, inhonogeneous terrain is used to compare calculated field strengths

with observed measurerrent.s for 9 actual paths and frequencies ranging from 120 kHz

to 50 MHz. All comparisons show encouraging agreement between calculations and

measurement. The 20 MHz comparisons over the Colorado MJuntains provided a

challenge for PRCGRAM. WAGlER.

16. Key Words '(Alphabetical order, separated by semicolons)

HF-VHF groundwave prediction; integral equation method; irregular terrain;

rreasurerrent canparisons; radio propagation. .

17. AVAILABILITY STATEMENT

ex UNLIMITED.

D FOR OFFICIAL DISTRIBUTION.

* u.s.GOVERNMENT PRINTING OFFICE:1979-680-195 I 484

18. Securi ty Class (This report)

Unclassified

19. Security Class (This page)

Unclassified

20. Number of pages

137

21. Price:

L'SCOMM-DC 29716-P73 .